11. a) Write 72 as the product of its prime factors. b) What are the composite factors of 72 ? c) Which factors of 72 are square numbers?

To express 72 as the product of its prime factors, we start with its factorization: 72 can be broken down into 8 and 9 (since 72 = 8 × 9). Then, we factor both of those: 8 = 2 × 2 × 2 (or \(2^3\)) and 9 = 3 × 3 (or \(3^2\)). So, we can write 72 as \(2^3 × 3^2\). The composite factors of 72 are those factors that are not prime and not just the number 1. The composite factors include: 4 (2 × 2), 6 (2 × 3), 8 (2 × 2 × 2), 9 (3 × 3), 12 (3 × 4), 18 (2 × 9), 24 (3 × 8), 36 (4 × 9), and the number 72 itself. The square numbers that are factors of 72 are 1 (since \(1^2 = 1\)), 4 (since \(2^2 = 4\)), and 36 (since \(6^2 = 36\)). These factors represent perfect squares derived from multiplying the same integer by itself.