Part B: Finding the HCF 4. Find the HCF of: a) 30 and 45 b) 50 and 125 c) 64 and 96 d) 72,96 , and 120

To find the HCF (Highest Common Factor) of these numbers, we can use the prime factorization method or list the factors. For 30 and 45, the prime factors are: 30 = 2 × 3 × 5 45 = 3 × 3 × 5 The common factors are 3 and 5, so the HCF is: 15. For 50 and 125, the prime factors are: 50 = 2 × 5 × 5 125 = 5 × 5 × 5 The only common factor is 5, so the HCF is: 5. For 64 and 96, the prime factors are: 64 = 2 × 2 × 2 × 2 × 2 × 2 (or 2^6) 96 = 2 × 2 × 2 × 2 × 2 × 3 (or 2^5 × 3) The HCF is 2 raised to the minimum power, 2^5, which equals 32. For 72, 96, and 120, the prime factors are: 72 = 2 × 2 × 2 × 3 × 3 (or 2^3 × 3^2) 96 = 2 × 2 × 2 × 2 × 3 (or 2^5 × 3) 120 = 2 × 2 × 2 × 5 × 3 (or 2^3 × 3 × 5) The common factors (with minimum powers) are 2^3 and 3^1, so the HCF is: 24.