Question

Use the Greatest Common Factor (GCF) to simplify the fraction. 65/91

Answer 1

To simplify the fraction \( \frac{65}{91} \) using the Greatest Common Factor (GCF), we first need to find the GCF of 65 and 91.

1. **Find the factors of 65**:
- The prime factorization of 65 is \( 5 \times 13 \).

2. **Find the factors of 91**:
- The prime factorization of 91 is \( 7 \times 13 \).

3. **Find the GCF**:
- The common factor between the two numbers is \( 13 \).

4. **Simplify the fraction**:
- Divide both the numerator and the denominator by their GCF (13):
\[
\frac{65 \div 13}{91 \div 13} = \frac{5}{7}.
\]

Thus, the simplified form of the fraction \( \frac{65}{91} \) is \( \frac{5}{7} \).