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

To find the highest common factor (HCF), also known as the greatest common divisor (GCD), of 72 and 96, we'll perform the prime factorization of both numbers and then identify the common factors with the smallest exponents. 1. **Prime Factorization:** - **96:** \( 96 = 2^5 \times 3 \) - **72:** \( 72 = 8 \times 9 = 2^3 \times 3^2 \) 2. **Identify Common Prime Factors:** - Both numbers have the prime factors 2 and 3. 3. **Determine the Lowest Exponents:** - For the prime number 2: - 96 has \( 2^5 \) - 72 has \( 2^3 \) - **Take the lower exponent:** \( 2^3 \) - For the prime number 3: - 96 has \( 3^1 \) - 72 has \( 3^2 \) - **Take the lower exponent:** \( 3^1 \) 4. **Calculate the HCF:** \[ \text{HCF} = 2^3 \times 3^1 = 8 \times 3 = 24 \] **Therefore, the highest common factor of 72 and 96 is 24.** **Answer:** 24