1. Beth is going to reduce the fraction \( \frac{124}{64} \). What is the greatest common factor of the numerator and the denominator?

To find the greatest common factor (GCF) of the numerator \(124\) and the denominator \(64\), we can start by finding the prime factorizations of both numbers. **Step 1: Factor \(124\)** We can divide \(124\) by \(2\) (the smallest prime number): \[ 124 \div 2 = 62 \] Next, we divide \(62\) by \(2\): \[ 62 \div 2 = 31 \] Now, \(31\) is a prime number. Therefore, the prime factorization of \(124\) is: \[ 124 = 2^2 \times 31 \] **Step 2: Factor \(64\)** Next, we factor \(64\): \[ 64 = 2 \times 32 \] \[ 32 = 2 \times 16 \] \[ 16 = 2 \times 8 \] \[ 8 = 2 \times 4 \] \[ 4 = 2 \times 2 \] Thus, we can express \(64\) as: \[ 64 = 2^6 \] **Step 3: Find the GCF** Now we have the prime factorizations: - \(124 = 2^2 \times 31\) - \(64 = 2^6\) To find the GCF, we take the lowest power of each common prime factor. The only common prime factor is \(2\). The lowest power of \(2\) in the factorizations is \(2^2\). Thus, the GCF of \(124\) and \(64\) is: \[ GCF = 2^2 = 4 \] Therefore, the greatest common factor of \(124\) and \(64\) is \(\boxed{4}\).