Question

The greatest common factor of 48 and 32 is

Answer 1

To find the greatest common factor (GCF) of 48 and 32, we can use the prime factorization method.

1. **Prime Factorization:**
- The prime factorization of 48 is:
\[
48 = 2^4 \times 3^1
\]
- The prime factorization of 32 is:
\[
32 = 2^5
\]

2. **Identify Common Factors:**
- The common prime factor is \(2\).
- The lowest exponent for the common prime factor \(2\) is \(4\) (from \(2^4\) in the factorization of 48).

3. **Calculate the GCF:**
\[
\text{GCF} = 2^4 = 16
\]

Thus, the greatest common factor of 48 and 32 is **16**.