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?

Let's solve each part step by step. a) Express 72 as the product of its prime factors.  • Start by dividing 72 by 2: 72 = 2 × 36.  • Divide 36 by 2: 36 = 2 × 18, so 72 = 2 × 2 × 18.  • Divide 18 by 2: 18 = 2 × 9, so 72 = 2 × 2 × 2 × 9.  • Recognize that 9 = 3 × 3.  • Thus, 72 = 2³ × 3². b) Find the composite factors of 72.  • First, determine all factors of 72. The factors are:    1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.  • Composite numbers are defined as numbers greater than 1 that are not prime.  • Remove 1 (neither prime nor composite) and the prime numbers 2 and 3:    Composite factors remain: 4, 6, 8, 9, 12, 18, 24, 36, 72. c) Identify which factors of 72 are square numbers.  • A perfect square is an integer that is the square of an integer.  • From the list of factors, the perfect squares are:    1 (1²), 4 (2²), 9 (3²), and 36 (6²). Summary of Answers: a) 72 = 2³ × 3². b) The composite factors of 72 are: 4, 6, 8, 9, 12, 18, 24, 36, and 72. c) The factors of 72 that are square numbers are: 1, 4, 9, and 36.