To simplify the fraction \( \frac{32}{160} \) using the Greatest Common Factor (GCF), we first need to find the GCF of the numerator (32) and the denominator (160).
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Find the GCF of 32 and 160:
- The prime factorization of 32 is \( 2^5 \) (since \( 32 = 2 \times 2 \times 2 \times 2 \times 2 \)).
- The prime factorization of 160 is \( 2^5 \times 5 \) (since \( 160 = 2 \times 2 \times 2 \times 2 \times 2 \times 5 \)).
- The GCF is determined by taking the lowest power of all common prime factors. Here, the common prime factor is \( 2 \) and the minimum exponent is \( 5 \).
- Therefore, \( \text{GCF}(32, 160) = 2^5 = 32 \).
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Divide both the numerator and the denominator by the GCF:
- \( \frac{32 \div 32}{160 \div 32} = \frac{1}{5} \).
Thus, the simplified form of \( \frac{32}{160} \) is \( \frac{1}{5} \).
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