Prime Time — Important Questions

4, 6, 9, 12

Factors of 36 are numbers that divide 36 exactly. Let's check: 36 ÷ 4 = 9 ✓, 36 ÷ 6 = 6 ✓, 36 ÷ 8 = 4.5 ✗, 36 ÷ 9 = 4 ✓, 36 ÷ 12 = 3 ✓, 36 ÷ 15 = 2.4 ✗. So factors are 4, 6, 9, and 12.

True

Two numbers are co-prime if their HCF is 1. Prime factorization: 15 = 3 × 5, 28 = 2² × 7. Since 15 and 28 have no common prime factors, they are co-prime. We can verify: factors of 15 are 1, 3, 5, 15 and factors of 28 are 1, 2, 4, 7, 14, 28. Only common factor is 1.

21, 27, 33

Composite numbers have more than 2 factors. Let's check: 21 = 3 × 7 (factors: 1, 3, 7, 21) - composite. 23 has only factors 1, 23 - prime. 27 = 3³ (factors: 1, 3, 9, 27) - composite. 29 has only factors 1, 29 - prime. 33 = 3 × 11 (factors: 1, 3, 11, 33) - composite.

False

This is false. If a number is divisible by both 4 and 6, it must be divisible by their LCM, not their product. LCM of 4 and 6 = 12 (since 4 = 2², 6 = 2 × 3, so LCM = 2² × 3 = 12). For example, 12 is divisible by both 4 and 6, but not by 24.