| id,topic,question,answer,working | |
| 1,HCF and LCM,Find the HCF and LCM of 36 and 48.,"HCF 12, LCM 144",HCF x LCM = 36x48 = 1728. | |
| 2,HCF and LCM,Find the HCF and LCM of 84 and 126.,"HCF 42, LCM 252",HCF x LCM = 84x126 = 10584. | |
| 3,HCF and LCM,Find the HCF and LCM of 150 and 225.,"HCF 75, LCM 450",HCF x LCM = 150x225 = 33750. | |
| 4,Unit digit,What is the unit digit of 7^95?,3,"Unit digits of powers of 7 cycle [7, 9, 3, 1]; 95 mod 4 = 3." | |
| 5,Unit digit,What is the unit digit of 3^102?,9,"Unit digits of powers of 3 cycle [3, 9, 7, 1]; 102 mod 4 = 2." | |
| 6,Unit digit,What is the unit digit of 2^57?,2,"Unit digits of powers of 2 cycle [2, 4, 8, 6]; 57 mod 4 = 1." | |
| 7,Unit digit,What is the unit digit of 9^41?,9,"Unit digits of powers of 9 cycle [9, 1, 9, 1]; 41 mod 4 = 1." | |
| 8,Remainders,Find the remainder when 2^31 is divided by 5.,3,"Powers of 2 mod 5 cycle 2, 4, 3, 1; 31 mod 4 = 3, so the remainder is 3." | |
| 9,Remainders,Find the remainder when 17^23 is divided by 16.,1,"17 leaves remainder 1 on division by 16, so 17^23 also leaves 1." | |
| 10,Remainders,Find the remainder when 10^20 + 7 is divided by 9.,8,"10 leaves remainder 1 on division by 9, so 10^20 leaves 1; 1 + 7 = 8." | |
| 11,Factors,How many positive factors does 360 have?,24,2^3 x 3^2 x 5^1 -> 4 x 3 x 2 = 24. | |
| 12,Factors,How many positive factors does 1000 have?,16,2^3 x 5^3 -> 4 x 4 = 16. | |
| 13,Factors,How many positive factors does 2310 have?,32,2^1 x 3^1 x 5^1 x 7^1 x 11^1 -> 2 x 2 x 2 x 2 x 2 = 32. | |