Factor the linear expression 30 d + 24 using the GCF

Answer 1

To factor the linear expression \(30d + 24\) using the greatest common factor (GCF), first, we need to determine the GCF of the coefficients \(30\) and \(24\).

1. Find the GCF of 30 and 24:

   • The factors of \(30\) are: \(1, 2, 3, 5, 6, 10, 15, 30\)
   • The factors of \(24\) are: \(1, 2, 3, 4, 6, 8, 12, 24\)
   • The common factors are: \(1, 2, 3, 6\)
   • The greatest common factor is \(6\).

2. Factor out the GCF:

   • Divide each term in the expression by the GCF:
   • \(30d \div 6 = 5d\)
   • \(24 \div 6 = 4\)

3. Write the factored expression: \[ 30d + 24 = 6(5d + 4) \]

Thus, the factored form of \(30d + 24\) using the GCF is: \[ 6(5d + 4) \]