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: \[ 8(3e + 4f) \]