To simplify the fraction \( \frac{65}{91} \) using the Greatest Common Factor (GCF), we first need to find the GCF of 65 and 91.
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Find the factors of 65:
- The prime factorization of 65 is \( 5 \times 13 \).
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Find the factors of 91:
- The prime factorization of 91 is \( 7 \times 13 \).
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Find the GCF:
- The common factor between the two numbers is \( 13 \).
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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 \( \frac{5}{7} \).
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