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: $$8(3e+4f)$$