(b) Given that \( 96=2^{5} \times 3 \), calculate the common factor of 72 and 96 .

To find the **common factor** of 72 and 96, we'll use their prime factorizations. You've already provided the prime factorization of 96: \[ 96 = 2^{5} \times 3 \] Let's determine the prime factorization of 72: \[ 72 = 8 \times 9 = 2^{3} \times 3^{2} \] **Step-by-Step Process:** 1. **Identify Common Prime Factors:** - **For 2:** - 96 has \(2^{5}\) - 72 has \(2^{3}\) - **Common exponent:** \( \min(5, 3) = 3 \) - **For 3:** - 96 has \(3^{1}\) - 72 has \(3^{2}\) - **Common exponent:** \( \min(1, 2) = 1 \) 2. **Multiply the Common Prime Factors:** \[ \text{Greatest Common Factor (GCF)} = 2^{3} \times 3^{1} = 8 \times 3 = 24 \] **Conclusion:** The greatest common factor of 72 and 96 is **24**.