Question

Factor 24e + 32f using the GCF.

Answer 1

To factor the expression \( 24e + 32f \) using the greatest common factor (GCF), we first need to determine the GCF of the coefficients:

1. **Identify the coefficients**: The coefficients are 24 and 32.
2. **Find the GCF of 24 and 32**:
- The prime factorization of 24 is \( 2^3 \times 3 \).
- The prime factorization of 32 is \( 2^5 \).
- The common factors are \( 2 \). The minimum exponent of \( 2 \) in both factorizations is \( 3 \).
- Thus, \( \text{GCF}(24, 32) = 2^3 = 8 \).

3. **Factor out the GCF**:
- Since the GCF is 8, we can factor it out of the expression:
\[
24e + 32f = 8(3e + 4f)
\]

Therefore, the factored form of \( 24e + 32f \) is:
\[
8(3e + 4f)
\]