Remove old v0.3/

v0.3/number_theory.jsonl

@@ -1,304 +0,0 @@
-{"problem": "Is 82 a prime number?", "solution": "82 is divisible by 2, so it is not prime.", "answer": "No", "topic": "number_theory.primes", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Is 20 a prime number?", "solution": "20 is divisible by 2, so it is not prime.", "answer": "No", "topic": "number_theory.primes", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Is 54 a prime number?", "solution": "54 is divisible by 2, so it is not prime.", "answer": "No", "topic": "number_theory.primes", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Find all positive factors of 57.", "solution": "The positive factors of 57 are 1, 3, 19, 57.", "answer": "1, 3, 19, 57", "topic": "number_theory.factors", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Find all positive factors of 60.", "solution": "The positive factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.", "answer": "1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60", "topic": "number_theory.factors", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Find all positive factors of 93.", "solution": "The positive factors of 93 are 1, 3, 31, 93.", "answer": "1, 3, 31, 93", "topic": "number_theory.factors", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Find all positive factors of 77.", "solution": "The positive factors of 77 are 1, 7, 11, 77.", "answer": "1, 7, 11, 77", "topic": "number_theory.factors", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Is 79 a prime number?", "solution": "79 has no positive divisors other than 1 and 79, so it is prime.", "answer": "Yes", "topic": "number_theory.primes", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Is 22 a prime number?", "solution": "22 is divisible by 2, so it is not prime.", "answer": "No", "topic": "number_theory.primes", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Find all positive factors of 56.", "solution": "The positive factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56.", "answer": "1, 2, 4, 7, 8, 14, 28, 56", "topic": "number_theory.factors", "difficulty": "medium", "education_level": "middle_school", "language": "en", "verification_status": "verified"}
-{"problem": "Is 46 a prime number?", "solution": "46 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000008"}
-{"problem": "Find the least common multiple (LCM) of 11 and 16.", "solution": "LCM(11, 16) = 176", "answer": "176", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000011"}
-{"problem": "Is 55 a prime number?", "solution": "55 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000018"}
-{"problem": "Is 73 a prime number?", "solution": "73 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000025"}
-{"problem": "Is 59 a prime number?", "solution": "59 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000032"}
-{"problem": "Find the greatest common divisor (GCD) of 97 and 93.", "solution": "GCD(97, 93) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000040"}
-{"problem": "Is 61 a prime number?", "solution": "61 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000063"}
-{"problem": "Find the least common multiple (LCM) of 16 and 7.", "solution": "LCM(16, 7) = 112", "answer": "112", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000064"}
-{"problem": "Find the greatest common divisor (GCD) of 24 and 39.", "solution": "GCD(24, 39) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000066"}
-{"problem": "Find the greatest common divisor (GCD) of 83 and 84.", "solution": "GCD(83, 84) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000072"}
-{"problem": "Find the least common multiple (LCM) of 20 and 10.", "solution": "LCM(20, 10) = 20", "answer": "20", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000074"}
-{"problem": "Find all positive factors of 14.", "solution": "The positive factors of 14 are: 1, 2, 7, 14", "answer": "1, 2, 7, 14", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000083"}
-{"problem": "Is 19 a prime number?", "solution": "19 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000112"}
-{"problem": "Find the least common multiple (LCM) of 11 and 19.", "solution": "LCM(11, 19) = 209", "answer": "209", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000118"}
-{"problem": "Find the least common multiple (LCM) of 13 and 6.", "solution": "LCM(13, 6) = 78", "answer": "78", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000119"}
-{"problem": "Find the greatest common divisor (GCD) of 68 and 45.", "solution": "GCD(68, 45) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000140"}
-{"problem": "Find the greatest common divisor (GCD) of 49 and 85.", "solution": "GCD(49, 85) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000144"}
-{"problem": "Is 18 a prime number?", "solution": "18 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000148"}
-{"problem": "Find the greatest common divisor (GCD) of 91 and 92.", "solution": "GCD(91, 92) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000155"}
-{"problem": "Find the greatest common divisor (GCD) of 65 and 17.", "solution": "GCD(65, 17) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000162"}
-{"problem": "Is 6 a prime number?", "solution": "6 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000166"}
-{"problem": "Is 98 a prime number?", "solution": "98 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000168"}
-{"problem": "Is 69 a prime number?", "solution": "69 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000176"}
-{"problem": "Find the greatest common divisor (GCD) of 74 and 29.", "solution": "GCD(74, 29) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000179"}
-{"problem": "Is 44 a prime number?", "solution": "44 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000191"}
-{"problem": "Find the least common multiple (LCM) of 25 and 13.", "solution": "LCM(25, 13) = 325", "answer": "325", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000204"}
-{"problem": "Is 89 a prime number?", "solution": "89 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000208"}
-{"problem": "Is 4 a prime number?", "solution": "4 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000216"}
-{"problem": "Find the least common multiple (LCM) of 9 and 29.", "solution": "LCM(9, 29) = 261", "answer": "261", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000224"}
-{"problem": "Find the greatest common divisor (GCD) of 38 and 12.", "solution": "GCD(38, 12) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000237"}
-{"problem": "Find the least common multiple (LCM) of 21 and 22.", "solution": "LCM(21, 22) = 462", "answer": "462", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000238"}
-{"problem": "Find all positive factors of 75.", "solution": "The positive factors of 75 are: 1, 3, 5, 15, 25, 75", "answer": "1, 3, 5, 15, 25, 75", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000240"}
-{"problem": "Find all positive factors of 26.", "solution": "The positive factors of 26 are: 1, 2, 13, 26", "answer": "1, 2, 13, 26", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000253"}
-{"problem": "Find the least common multiple (LCM) of 6 and 14.", "solution": "LCM(6, 14) = 42", "answer": "42", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000262"}
-{"problem": "Find the least common multiple (LCM) of 24 and 26.", "solution": "LCM(24, 26) = 312", "answer": "312", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000268"}
-{"problem": "Find the least common multiple (LCM) of 27 and 23.", "solution": "LCM(27, 23) = 621", "answer": "621", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000277"}
-{"problem": "Find all positive factors of 66.", "solution": "The positive factors of 66 are: 1, 2, 3, 6, 11, 22, 33, 66", "answer": "1, 2, 3, 6, 11, 22, 33, 66", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000293"}
-{"problem": "Find the least common multiple (LCM) of 15 and 13.", "solution": "LCM(15, 13) = 195", "answer": "195", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000317"}
-{"problem": "Find the greatest common divisor (GCD) of 71 and 79.", "solution": "GCD(71, 79) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000324"}
-{"problem": "Is 13 a prime number?", "solution": "13 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000331"}
-{"problem": "Find the greatest common divisor (GCD) of 72 and 93.", "solution": "GCD(72, 93) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000340"}
-{"problem": "Find the greatest common divisor (GCD) of 70 and 62.", "solution": "GCD(70, 62) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000342"}
-{"problem": "Is 88 a prime number?", "solution": "88 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000344"}
-{"problem": "Find all positive factors of 53.", "solution": "The positive factors of 53 are: 1, 53", "answer": "1, 53", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000370"}
-{"problem": "Find the greatest common divisor (GCD) of 13 and 98.", "solution": "GCD(13, 98) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000372"}
-{"problem": "Find the least common multiple (LCM) of 7 and 20.", "solution": "LCM(7, 20) = 140", "answer": "140", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000373"}
-{"problem": "Find the greatest common divisor (GCD) of 73 and 47.", "solution": "GCD(73, 47) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000374"}
-{"problem": "Find all positive factors of 17.", "solution": "The positive factors of 17 are: 1, 17", "answer": "1, 17", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000392"}
-{"problem": "Is 72 a prime number?", "solution": "72 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000404"}
-{"problem": "Is 29 a prime number?", "solution": "29 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000431"}
-{"problem": "Find the least common multiple (LCM) of 24 and 2.", "solution": "LCM(24, 2) = 24", "answer": "24", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000443"}
-{"problem": "Find the greatest common divisor (GCD) of 21 and 93.", "solution": "GCD(21, 93) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000448"}
-{"problem": "Is 38 a prime number?", "solution": "38 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000455"}
-{"problem": "Is 41 a prime number?", "solution": "41 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000468"}
-{"problem": "Find the greatest common divisor (GCD) of 66 and 61.", "solution": "GCD(66, 61) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000472"}
-{"problem": "Find the greatest common divisor (GCD) of 38 and 33.", "solution": "GCD(38, 33) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000473"}
-{"problem": "Find the greatest common divisor (GCD) of 74 and 23.", "solution": "GCD(74, 23) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000480"}
-{"problem": "Find the least common multiple (LCM) of 15 and 3.", "solution": "LCM(15, 3) = 15", "answer": "15", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000490"}
-{"problem": "Find the least common multiple (LCM) of 12 and 25.", "solution": "LCM(12, 25) = 300", "answer": "300", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000491"}
-{"problem": "Find the greatest common divisor (GCD) of 78 and 53.", "solution": "GCD(78, 53) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000493"}
-{"problem": "Find all positive factors of 20.", "solution": "The positive factors of 20 are: 1, 2, 4, 5, 10, 20", "answer": "1, 2, 4, 5, 10, 20", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000495"}
-{"problem": "Find all positive factors of 91.", "solution": "The positive factors of 91 are: 1, 7, 13, 91", "answer": "1, 7, 13, 91", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000503"}
-{"problem": "Find the greatest common divisor (GCD) of 89 and 76.", "solution": "GCD(89, 76) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000512"}
-{"problem": "Find the greatest common divisor (GCD) of 53 and 67.", "solution": "GCD(53, 67) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000516"}
-{"problem": "Find the greatest common divisor (GCD) of 40 and 100.", "solution": "GCD(40, 100) = 20", "answer": "20", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000521"}
-{"problem": "Is 40 a prime number?", "solution": "40 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000536"}
-{"problem": "Is 68 a prime number?", "solution": "68 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000537"}
-{"problem": "Find the greatest common divisor (GCD) of 17 and 37.", "solution": "GCD(17, 37) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000539"}
-{"problem": "Find the greatest common divisor (GCD) of 39 and 52.", "solution": "GCD(39, 52) = 13", "answer": "13", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000548"}
-{"problem": "Is 3 a prime number?", "solution": "3 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000553"}
-{"problem": "Find the least common multiple (LCM) of 9 and 28.", "solution": "LCM(9, 28) = 252", "answer": "252", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000554"}
-{"problem": "Find the greatest common divisor (GCD) of 34 and 78.", "solution": "GCD(34, 78) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000556"}
-{"problem": "Find the least common multiple (LCM) of 4 and 27.", "solution": "LCM(4, 27) = 108", "answer": "108", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000562"}
-{"problem": "Find the greatest common divisor (GCD) of 78 and 80.", "solution": "GCD(78, 80) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000576"}
-{"problem": "Find all positive factors of 45.", "solution": "The positive factors of 45 are: 1, 3, 5, 9, 15, 45", "answer": "1, 3, 5, 9, 15, 45", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000584"}
-{"problem": "Find the least common multiple (LCM) of 17 and 10.", "solution": "LCM(17, 10) = 170", "answer": "170", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000585"}
-{"problem": "Find all positive factors of 69.", "solution": "The positive factors of 69 are: 1, 3, 23, 69", "answer": "1, 3, 23, 69", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000591"}
-{"problem": "Find all positive factors of 86.", "solution": "The positive factors of 86 are: 1, 2, 43, 86", "answer": "1, 2, 43, 86", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000596"}
-{"problem": "Find all positive factors of 70.", "solution": "The positive factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70", "answer": "1, 2, 5, 7, 10, 14, 35, 70", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000598"}
-{"problem": "Find all positive factors of 68.", "solution": "The positive factors of 68 are: 1, 2, 4, 17, 34, 68", "answer": "1, 2, 4, 17, 34, 68", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000621"}
-{"problem": "Find the least common multiple (LCM) of 26 and 23.", "solution": "LCM(26, 23) = 598", "answer": "598", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000624"}
-{"problem": "Is 90 a prime number?", "solution": "90 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000631"}
-{"problem": "Find all positive factors of 80.", "solution": "The positive factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80", "answer": "1, 2, 4, 5, 8, 10, 16, 20, 40, 80", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000647"}
-{"problem": "Find the least common multiple (LCM) of 17 and 3.", "solution": "LCM(17, 3) = 51", "answer": "51", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000649"}
-{"problem": "Find the least common multiple (LCM) of 8 and 19.", "solution": "LCM(8, 19) = 152", "answer": "152", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000659"}
-{"problem": "Find the greatest common divisor (GCD) of 75 and 75.", "solution": "GCD(75, 75) = 75", "answer": "75", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000670"}
-{"problem": "Find all positive factors of 37.", "solution": "The positive factors of 37 are: 1, 37", "answer": "1, 37", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000673"}
-{"problem": "Find all positive factors of 94.", "solution": "The positive factors of 94 are: 1, 2, 47, 94", "answer": "1, 2, 47, 94", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000686"}
-{"problem": "Find the least common multiple (LCM) of 25 and 21.", "solution": "LCM(25, 21) = 525", "answer": "525", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000689"}
-{"problem": "Find all positive factors of 27.", "solution": "The positive factors of 27 are: 1, 3, 9, 27", "answer": "1, 3, 9, 27", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000692"}
-{"problem": "Find all positive factors of 54.", "solution": "The positive factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54", "answer": "1, 2, 3, 6, 9, 18, 27, 54", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000694"}
-{"problem": "Is 83 a prime number?", "solution": "83 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000701"}
-{"problem": "Find the greatest common divisor (GCD) of 15 and 91.", "solution": "GCD(15, 91) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000703"}
-{"problem": "Is 77 a prime number?", "solution": "77 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000706"}
-{"problem": "Find the least common multiple (LCM) of 14 and 18.", "solution": "LCM(14, 18) = 126", "answer": "126", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000713"}
-{"problem": "Find the greatest common divisor (GCD) of 31 and 12.", "solution": "GCD(31, 12) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000714"}
-{"problem": "Find the least common multiple (LCM) of 5 and 13.", "solution": "LCM(5, 13) = 65", "answer": "65", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000716"}
-{"problem": "Find the least common multiple (LCM) of 20 and 29.", "solution": "LCM(20, 29) = 580", "answer": "580", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000724"}
-{"problem": "Find the greatest common divisor (GCD) of 16 and 92.", "solution": "GCD(16, 92) = 4", "answer": "4", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000729"}
-{"problem": "Find the greatest common divisor (GCD) of 89 and 60.", "solution": "GCD(89, 60) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000734"}
-{"problem": "Find all positive factors of 28.", "solution": "The positive factors of 28 are: 1, 2, 4, 7, 14, 28", "answer": "1, 2, 4, 7, 14, 28", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000736"}
-{"problem": "Find all positive factors of 16.", "solution": "The positive factors of 16 are: 1, 2, 4, 8, 16", "answer": "1, 2, 4, 8, 16", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000739"}
-{"problem": "Find the greatest common divisor (GCD) of 47 and 14.", "solution": "GCD(47, 14) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000742"}
-{"problem": "Find the greatest common divisor (GCD) of 21 and 16.", "solution": "GCD(21, 16) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000745"}
-{"problem": "Find the greatest common divisor (GCD) of 16 and 72.", "solution": "GCD(16, 72) = 8", "answer": "8", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000746"}
-{"problem": "Find all positive factors of 48.", "solution": "The positive factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48", "answer": "1, 2, 3, 4, 6, 8, 12, 16, 24, 48", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000751"}
-{"problem": "Is 81 a prime number?", "solution": "81 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000764"}
-{"problem": "Find the greatest common divisor (GCD) of 74 and 79.", "solution": "GCD(74, 79) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000765"}
-{"problem": "Find the greatest common divisor (GCD) of 45 and 65.", "solution": "GCD(45, 65) = 5", "answer": "5", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000773"}
-{"problem": "Is 100 a prime number?", "solution": "100 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000776"}
-{"problem": "Find the greatest common divisor (GCD) of 93 and 30.", "solution": "GCD(93, 30) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000779"}
-{"problem": "Find all positive factors of 51.", "solution": "The positive factors of 51 are: 1, 3, 17, 51", "answer": "1, 3, 17, 51", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000784"}
-{"problem": "Find all positive factors of 61.", "solution": "The positive factors of 61 are: 1, 61", "answer": "1, 61", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000785"}
-{"problem": "Find the greatest common divisor (GCD) of 21 and 90.", "solution": "GCD(21, 90) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000788"}
-{"problem": "Find the least common multiple (LCM) of 11 and 23.", "solution": "LCM(11, 23) = 253", "answer": "253", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000796"}
-{"problem": "Find the greatest common divisor (GCD) of 54 and 80.", "solution": "GCD(54, 80) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000802"}
-{"problem": "Find the least common multiple (LCM) of 7 and 23.", "solution": "LCM(7, 23) = 161", "answer": "161", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000804"}
-{"problem": "Is 67 a prime number?", "solution": "67 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000818"}
-{"problem": "Find the greatest common divisor (GCD) of 43 and 78.", "solution": "GCD(43, 78) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000821"}
-{"problem": "Is 31 a prime number?", "solution": "31 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000825"}
-{"problem": "Is 84 a prime number?", "solution": "84 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000836"}
-{"problem": "Find the greatest common divisor (GCD) of 44 and 66.", "solution": "GCD(44, 66) = 22", "answer": "22", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000845"}
-{"problem": "Find the greatest common divisor (GCD) of 52 and 65.", "solution": "GCD(52, 65) = 13", "answer": "13", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000854"}
-{"problem": "Is 30 a prime number?", "solution": "30 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000855"}
-{"problem": "Find the greatest common divisor (GCD) of 39 and 32.", "solution": "GCD(39, 32) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000859"}
-{"problem": "Find the greatest common divisor (GCD) of 68 and 87.", "solution": "GCD(68, 87) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000870"}
-{"problem": "Find all positive factors of 39.", "solution": "The positive factors of 39 are: 1, 3, 13, 39", "answer": "1, 3, 13, 39", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000872"}
-{"problem": "Find all positive factors of 88.", "solution": "The positive factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88", "answer": "1, 2, 4, 8, 11, 22, 44, 88", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000873"}
-{"problem": "Find the greatest common divisor (GCD) of 29 and 65.", "solution": "GCD(29, 65) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000881"}
-{"problem": "Find all positive factors of 25.", "solution": "The positive factors of 25 are: 1, 5, 25", "answer": "1, 5, 25", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000883"}
-{"problem": "Find all positive factors of 31.", "solution": "The positive factors of 31 are: 1, 31", "answer": "1, 31", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000894"}
-{"problem": "Find all positive factors of 95.", "solution": "The positive factors of 95 are: 1, 5, 19, 95", "answer": "1, 5, 19, 95", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000896"}
-{"problem": "Is 17 a prime number?", "solution": "17 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000900"}
-{"problem": "Find the least common multiple (LCM) of 25 and 9.", "solution": "LCM(25, 9) = 225", "answer": "225", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000906"}
-{"problem": "Find all positive factors of 98.", "solution": "The positive factors of 98 are: 1, 2, 7, 14, 49, 98", "answer": "1, 2, 7, 14, 49, 98", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000921"}
-{"problem": "Find all positive factors of 67.", "solution": "The positive factors of 67 are: 1, 67", "answer": "1, 67", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000924"}
-{"problem": "Is 23 a prime number?", "solution": "23 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000927"}
-{"problem": "Find the greatest common divisor (GCD) of 87 and 20.", "solution": "GCD(87, 20) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000928"}
-{"problem": "Is 42 a prime number?", "solution": "42 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000934"}
-{"problem": "Find the greatest common divisor (GCD) of 99 and 60.", "solution": "GCD(99, 60) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000941"}
-{"problem": "Find all positive factors of 83.", "solution": "The positive factors of 83 are: 1, 83", "answer": "1, 83", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000944"}
-{"problem": "Is 5 a prime number?", "solution": "5 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000957"}
-{"problem": "Find the least common multiple (LCM) of 27 and 6.", "solution": "LCM(27, 6) = 54", "answer": "54", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000967"}
-{"problem": "Find the greatest common divisor (GCD) of 67 and 77.", "solution": "GCD(67, 77) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000968"}
-{"problem": "Find the least common multiple (LCM) of 3 and 13.", "solution": "LCM(3, 13) = 39", "answer": "39", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000971"}
-{"problem": "Is 35 a prime number?", "solution": "35 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000979"}
-{"problem": "Find the least common multiple (LCM) of 28 and 30.", "solution": "LCM(28, 30) = 420", "answer": "420", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_000982"}
-{"problem": "Find all positive factors of 22.", "solution": "The positive factors of 22 are: 1, 2, 11, 22", "answer": "1, 2, 11, 22", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001009"}
-{"problem": "Find the greatest common divisor (GCD) of 13 and 48.", "solution": "GCD(13, 48) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001012"}
-{"problem": "Find the least common multiple (LCM) of 8 and 25.", "solution": "LCM(8, 25) = 200", "answer": "200", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001019"}
-{"problem": "Find the greatest common divisor (GCD) of 24 and 13.", "solution": "GCD(24, 13) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001029"}
-{"problem": "Find the greatest common divisor (GCD) of 19 and 72.", "solution": "GCD(19, 72) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001037"}
-{"problem": "Find the greatest common divisor (GCD) of 29 and 16.", "solution": "GCD(29, 16) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001038"}
-{"problem": "Find the greatest common divisor (GCD) of 21 and 23.", "solution": "GCD(21, 23) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001040"}
-{"problem": "Is 21 a prime number?", "solution": "21 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001047"}
-{"problem": "Is 45 a prime number?", "solution": "45 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001050"}
-{"problem": "Find the greatest common divisor (GCD) of 70 and 25.", "solution": "GCD(70, 25) = 5", "answer": "5", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001051"}
-{"problem": "Find the least common multiple (LCM) of 29 and 26.", "solution": "LCM(29, 26) = 754", "answer": "754", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001061"}
-{"problem": "Find all positive factors of 35.", "solution": "The positive factors of 35 are: 1, 5, 7, 35", "answer": "1, 5, 7, 35", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001070"}
-{"problem": "Find the least common multiple (LCM) of 6 and 26.", "solution": "LCM(6, 26) = 78", "answer": "78", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001081"}
-{"problem": "Is 34 a prime number?", "solution": "34 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001087"}
-{"problem": "Find all positive factors of 36.", "solution": "The positive factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36", "answer": "1, 2, 3, 4, 6, 9, 12, 18, 36", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001090"}
-{"problem": "Find the greatest common divisor (GCD) of 100 and 73.", "solution": "GCD(100, 73) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001100"}
-{"problem": "Find the greatest common divisor (GCD) of 15 and 72.", "solution": "GCD(15, 72) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001101"}
-{"problem": "Find all positive factors of 50.", "solution": "The positive factors of 50 are: 1, 2, 5, 10, 25, 50", "answer": "1, 2, 5, 10, 25, 50", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001118"}
-{"problem": "Find the greatest common divisor (GCD) of 27 and 36.", "solution": "GCD(27, 36) = 9", "answer": "9", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001132"}
-{"problem": "Find the least common multiple (LCM) of 3 and 26.", "solution": "LCM(3, 26) = 78", "answer": "78", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001133"}
-{"problem": "Find the greatest common divisor (GCD) of 12 and 91.", "solution": "GCD(12, 91) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001137"}
-{"problem": "Find the greatest common divisor (GCD) of 56 and 73.", "solution": "GCD(56, 73) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001143"}
-{"problem": "Find the least common multiple (LCM) of 23 and 8.", "solution": "LCM(23, 8) = 184", "answer": "184", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001147"}
-{"problem": "Find the greatest common divisor (GCD) of 73 and 97.", "solution": "GCD(73, 97) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001155"}
-{"problem": "Is 8 a prime number?", "solution": "8 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001178"}
-{"problem": "Find the greatest common divisor (GCD) of 37 and 39.", "solution": "GCD(37, 39) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001183"}
-{"problem": "Is 92 a prime number?", "solution": "92 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001184"}
-{"problem": "Find all positive factors of 46.", "solution": "The positive factors of 46 are: 1, 2, 23, 46", "answer": "1, 2, 23, 46", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001187"}
-{"problem": "Find the least common multiple (LCM) of 2 and 5.", "solution": "LCM(2, 5) = 10", "answer": "10", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001188"}
-{"problem": "Find the greatest common divisor (GCD) of 12 and 44.", "solution": "GCD(12, 44) = 4", "answer": "4", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001195"}
-{"problem": "Find the least common multiple (LCM) of 22 and 25.", "solution": "LCM(22, 25) = 550", "answer": "550", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001197"}
-{"problem": "Find the least common multiple (LCM) of 19 and 2.", "solution": "LCM(19, 2) = 38", "answer": "38", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001198"}
-{"problem": "Find the least common multiple (LCM) of 26 and 6.", "solution": "LCM(26, 6) = 78", "answer": "78", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001201"}
-{"problem": "Find the greatest common divisor (GCD) of 30 and 65.", "solution": "GCD(30, 65) = 5", "answer": "5", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001202"}
-{"problem": "Find the greatest common divisor (GCD) of 12 and 75.", "solution": "GCD(12, 75) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001227"}
-{"problem": "Find all positive factors of 99.", "solution": "The positive factors of 99 are: 1, 3, 9, 11, 33, 99", "answer": "1, 3, 9, 11, 33, 99", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001241"}
-{"problem": "Find the greatest common divisor (GCD) of 52 and 69.", "solution": "GCD(52, 69) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001249"}
-{"problem": "Find the greatest common divisor (GCD) of 24 and 76.", "solution": "GCD(24, 76) = 4", "answer": "4", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001252"}
-{"problem": "Find the least common multiple (LCM) of 27 and 27.", "solution": "LCM(27, 27) = 27", "answer": "27", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001255"}
-{"problem": "Find the least common multiple (LCM) of 5 and 14.", "solution": "LCM(5, 14) = 70", "answer": "70", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001256"}
-{"problem": "Find the least common multiple (LCM) of 5 and 16.", "solution": "LCM(5, 16) = 80", "answer": "80", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001261"}
-{"problem": "Find the least common multiple (LCM) of 30 and 27.", "solution": "LCM(30, 27) = 270", "answer": "270", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001269"}
-{"problem": "Find the greatest common divisor (GCD) of 37 and 75.", "solution": "GCD(37, 75) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001290"}
-{"problem": "Find the greatest common divisor (GCD) of 33 and 46.", "solution": "GCD(33, 46) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001298"}
-{"problem": "Find all positive factors of 44.", "solution": "The positive factors of 44 are: 1, 2, 4, 11, 22, 44", "answer": "1, 2, 4, 11, 22, 44", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001303"}
-{"problem": "Find the greatest common divisor (GCD) of 98 and 65.", "solution": "GCD(98, 65) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001304"}
-{"problem": "Find the least common multiple (LCM) of 21 and 20.", "solution": "LCM(21, 20) = 420", "answer": "420", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001314"}
-{"problem": "Find the greatest common divisor (GCD) of 76 and 35.", "solution": "GCD(76, 35) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001316"}
-{"problem": "Find the least common multiple (LCM) of 2 and 17.", "solution": "LCM(2, 17) = 34", "answer": "34", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001319"}
-{"problem": "Is 86 a prime number?", "solution": "86 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001339"}
-{"problem": "Is 28 a prime number?", "solution": "28 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001340"}
-{"problem": "Find the least common multiple (LCM) of 13 and 26.", "solution": "LCM(13, 26) = 26", "answer": "26", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001343"}
-{"problem": "Find all positive factors of 85.", "solution": "The positive factors of 85 are: 1, 5, 17, 85", "answer": "1, 5, 17, 85", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001348"}
-{"problem": "Is 57 a prime number?", "solution": "57 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001362"}
-{"problem": "Find the greatest common divisor (GCD) of 84 and 72.", "solution": "GCD(84, 72) = 12", "answer": "12", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001365"}
-{"problem": "Find the greatest common divisor (GCD) of 93 and 24.", "solution": "GCD(93, 24) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001371"}
-{"problem": "Find the least common multiple (LCM) of 21 and 15.", "solution": "LCM(21, 15) = 105", "answer": "105", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001373"}
-{"problem": "Find the least common multiple (LCM) of 24 and 18.", "solution": "LCM(24, 18) = 72", "answer": "72", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001377"}
-{"problem": "Find the greatest common divisor (GCD) of 56 and 93.", "solution": "GCD(56, 93) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001379"}
-{"problem": "Find the greatest common divisor (GCD) of 60 and 51.", "solution": "GCD(60, 51) = 3", "answer": "3", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001382"}
-{"problem": "Find the greatest common divisor (GCD) of 56 and 41.", "solution": "GCD(56, 41) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001384"}
-{"problem": "Find the least common multiple (LCM) of 29 and 13.", "solution": "LCM(29, 13) = 377", "answer": "377", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001395"}
-{"problem": "Find the least common multiple (LCM) of 3 and 7.", "solution": "LCM(3, 7) = 21", "answer": "21", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001403"}
-{"problem": "Is 50 a prime number?", "solution": "50 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001407"}
-{"problem": "Find all positive factors of 55.", "solution": "The positive factors of 55 are: 1, 5, 11, 55", "answer": "1, 5, 11, 55", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001418"}
-{"problem": "Find the least common multiple (LCM) of 15 and 18.", "solution": "LCM(15, 18) = 90", "answer": "90", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001442"}
-{"problem": "Find the greatest common divisor (GCD) of 24 and 25.", "solution": "GCD(24, 25) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001452"}
-{"problem": "Find the greatest common divisor (GCD) of 81 and 68.", "solution": "GCD(81, 68) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001453"}
-{"problem": "Find the least common multiple (LCM) of 29 and 8.", "solution": "LCM(29, 8) = 232", "answer": "232", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001458"}
-{"problem": "Is 2 a prime number?", "solution": "2 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001459"}
-{"problem": "Find the least common multiple (LCM) of 14 and 23.", "solution": "LCM(14, 23) = 322", "answer": "322", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001470"}
-{"problem": "Find the greatest common divisor (GCD) of 71 and 64.", "solution": "GCD(71, 64) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001485"}
-{"problem": "Find the least common multiple (LCM) of 13 and 9.", "solution": "LCM(13, 9) = 117", "answer": "117", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001492"}
-{"problem": "Find the least common multiple (LCM) of 2 and 14.", "solution": "LCM(2, 14) = 14", "answer": "14", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001493"}
-{"problem": "Find the least common multiple (LCM) of 13 and 28.", "solution": "LCM(13, 28) = 364", "answer": "364", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001502"}
-{"problem": "Find the greatest common divisor (GCD) of 18 and 91.", "solution": "GCD(18, 91) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001514"}
-{"problem": "Find the greatest common divisor (GCD) of 15 and 90.", "solution": "GCD(15, 90) = 15", "answer": "15", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001530"}
-{"problem": "Is 11 a prime number?", "solution": "11 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001532"}
-{"problem": "Find all positive factors of 40.", "solution": "The positive factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40", "answer": "1, 2, 4, 5, 8, 10, 20, 40", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001539"}
-{"problem": "Find the greatest common divisor (GCD) of 49 and 21.", "solution": "GCD(49, 21) = 7", "answer": "7", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001554"}
-{"problem": "Find the least common multiple (LCM) of 19 and 10.", "solution": "LCM(19, 10) = 190", "answer": "190", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001555"}
-{"problem": "Find the greatest common divisor (GCD) of 57 and 64.", "solution": "GCD(57, 64) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001559"}
-{"problem": "Find all positive factors of 79.", "solution": "The positive factors of 79 are: 1, 79", "answer": "1, 79", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001561"}
-{"problem": "Find the least common multiple (LCM) of 17 and 30.", "solution": "LCM(17, 30) = 510", "answer": "510", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001563"}
-{"problem": "Find the greatest common divisor (GCD) of 31 and 66.", "solution": "GCD(31, 66) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001576"}
-{"problem": "Find all positive factors of 29.", "solution": "The positive factors of 29 are: 1, 29", "answer": "1, 29", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001584"}
-{"problem": "Is 7 a prime number?", "solution": "7 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001586"}
-{"problem": "Find the greatest common divisor (GCD) of 40 and 14.", "solution": "GCD(40, 14) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001587"}
-{"problem": "Find the greatest common divisor (GCD) of 17 and 72.", "solution": "GCD(17, 72) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001591"}
-{"problem": "Is 99 a prime number?", "solution": "99 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001614"}
-{"problem": "Find all positive factors of 90.", "solution": "The positive factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90", "answer": "1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001616"}
-{"problem": "Find the greatest common divisor (GCD) of 17 and 30.", "solution": "GCD(17, 30) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001620"}
-{"problem": "Is 95 a prime number?", "solution": "95 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001625"}
-{"problem": "Find the least common multiple (LCM) of 7 and 21.", "solution": "LCM(7, 21) = 21", "answer": "21", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001627"}
-{"problem": "Find the greatest common divisor (GCD) of 90 and 90.", "solution": "GCD(90, 90) = 90", "answer": "90", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001633"}
-{"problem": "Find the greatest common divisor (GCD) of 95 and 99.", "solution": "GCD(95, 99) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001640"}
-{"problem": "Find all positive factors of 58.", "solution": "The positive factors of 58 are: 1, 2, 29, 58", "answer": "1, 2, 29, 58", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001646"}
-{"problem": "Find the greatest common divisor (GCD) of 59 and 23.", "solution": "GCD(59, 23) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001647"}
-{"problem": "Find the greatest common divisor (GCD) of 46 and 28.", "solution": "GCD(46, 28) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001651"}
-{"problem": "Find all positive factors of 18.", "solution": "The positive factors of 18 are: 1, 2, 3, 6, 9, 18", "answer": "1, 2, 3, 6, 9, 18", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001652"}
-{"problem": "Is 62 a prime number?", "solution": "62 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001660"}
-{"problem": "Find all positive factors of 65.", "solution": "The positive factors of 65 are: 1, 5, 13, 65", "answer": "1, 5, 13, 65", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001674"}
-{"problem": "Find the greatest common divisor (GCD) of 49 and 74.", "solution": "GCD(49, 74) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001686"}
-{"problem": "Find the least common multiple (LCM) of 5 and 24.", "solution": "LCM(5, 24) = 120", "answer": "120", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001690"}
-{"problem": "Find the least common multiple (LCM) of 29 and 10.", "solution": "LCM(29, 10) = 290", "answer": "290", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001694"}
-{"problem": "Is 85 a prime number?", "solution": "85 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001695"}
-{"problem": "Find the least common multiple (LCM) of 28 and 12.", "solution": "LCM(28, 12) = 84", "answer": "84", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001697"}
-{"problem": "Is 51 a prime number?", "solution": "51 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001711"}
-{"problem": "Is 96 a prime number?", "solution": "96 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001712"}
-{"problem": "Find the greatest common divisor (GCD) of 19 and 15.", "solution": "GCD(19, 15) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001719"}
-{"problem": "Find the greatest common divisor (GCD) of 47 and 48.", "solution": "GCD(47, 48) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001724"}
-{"problem": "Find the greatest common divisor (GCD) of 98 and 52.", "solution": "GCD(98, 52) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001728"}
-{"problem": "Find all positive factors of 41.", "solution": "The positive factors of 41 are: 1, 41", "answer": "1, 41", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001743"}
-{"problem": "Find all positive factors of 47.", "solution": "The positive factors of 47 are: 1, 47", "answer": "1, 47", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001750"}
-{"problem": "Find the greatest common divisor (GCD) of 91 and 81.", "solution": "GCD(91, 81) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001762"}
-{"problem": "Is 53 a prime number?", "solution": "53 is prime.", "answer": "prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001767"}
-{"problem": "Find the greatest common divisor (GCD) of 31 and 38.", "solution": "GCD(31, 38) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001768"}
-{"problem": "Find the least common multiple (LCM) of 15 and 5.", "solution": "LCM(15, 5) = 15", "answer": "15", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001776"}
-{"problem": "Find the greatest common divisor (GCD) of 26 and 93.", "solution": "GCD(26, 93) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001787"}
-{"problem": "Find the least common multiple (LCM) of 13 and 2.", "solution": "LCM(13, 2) = 26", "answer": "26", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001811"}
-{"problem": "Is 26 a prime number?", "solution": "26 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001837"}
-{"problem": "Find the greatest common divisor (GCD) of 36 and 13.", "solution": "GCD(36, 13) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001847"}
-{"problem": "Find the greatest common divisor (GCD) of 82 and 22.", "solution": "GCD(82, 22) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001849"}
-{"problem": "Find the greatest common divisor (GCD) of 50 and 99.", "solution": "GCD(50, 99) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001851"}
-{"problem": "Find the greatest common divisor (GCD) of 62 and 79.", "solution": "GCD(62, 79) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001859"}
-{"problem": "Find all positive factors of 38.", "solution": "The positive factors of 38 are: 1, 2, 19, 38", "answer": "1, 2, 19, 38", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001863"}
-{"problem": "Find the least common multiple (LCM) of 18 and 17.", "solution": "LCM(18, 17) = 306", "answer": "306", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001866"}
-{"problem": "Find the greatest common divisor (GCD) of 97 and 79.", "solution": "GCD(97, 79) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001870"}
-{"problem": "Find the greatest common divisor (GCD) of 76 and 72.", "solution": "GCD(76, 72) = 4", "answer": "4", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001872"}
-{"problem": "Find the greatest common divisor (GCD) of 56 and 39.", "solution": "GCD(56, 39) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001875"}
-{"problem": "Find the least common multiple (LCM) of 29 and 28.", "solution": "LCM(29, 28) = 812", "answer": "812", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001886"}
-{"problem": "Find all positive factors of 62.", "solution": "The positive factors of 62 are: 1, 2, 31, 62", "answer": "1, 2, 31, 62", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001888"}
-{"problem": "Find the greatest common divisor (GCD) of 49 and 77.", "solution": "GCD(49, 77) = 7", "answer": "7", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001891"}
-{"problem": "Find the least common multiple (LCM) of 14 and 29.", "solution": "LCM(14, 29) = 406", "answer": "406", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001898"}
-{"problem": "Find the greatest common divisor (GCD) of 50 and 87.", "solution": "GCD(50, 87) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001900"}
-{"problem": "Is 49 a prime number?", "solution": "49 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001909"}
-{"problem": "Find the greatest common divisor (GCD) of 31 and 81.", "solution": "GCD(31, 81) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001916"}
-{"problem": "Is 52 a prime number?", "solution": "52 is not prime.", "answer": "not prime", "topic": "number_theory.primes", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001923"}
-{"problem": "Find the greatest common divisor (GCD) of 21 and 17.", "solution": "GCD(21, 17) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001926"}
-{"problem": "Find the least common multiple (LCM) of 4 and 24.", "solution": "LCM(4, 24) = 24", "answer": "24", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001940"}
-{"problem": "Find the greatest common divisor (GCD) of 33 and 34.", "solution": "GCD(33, 34) = 1", "answer": "1", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001947"}
-{"problem": "Find all positive factors of 73.", "solution": "The positive factors of 73 are: 1, 73", "answer": "1, 73", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001954"}
-{"problem": "Find the least common multiple (LCM) of 20 and 12.", "solution": "LCM(20, 12) = 60", "answer": "60", "topic": "number_theory.lcm", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001957"}
-{"problem": "Find the greatest common divisor (GCD) of 30 and 88.", "solution": "GCD(30, 88) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001964"}
-{"problem": "Find all positive factors of 84.", "solution": "The positive factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84", "answer": "1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001987"}
-{"problem": "Find all positive factors of 43.", "solution": "The positive factors of 43 are: 1, 43", "answer": "1, 43", "topic": "number_theory.factors", "difficulty": "easy", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001993"}
-{"problem": "Find the greatest common divisor (GCD) of 50 and 88.", "solution": "GCD(50, 88) = 2", "answer": "2", "topic": "number_theory.gcd", "difficulty": "medium", "education_level": "middle_school", "language": "en", "source": "synthetic", "verification_status": "verified", "id": "omd_001996"}