Factor 48y+36z using GCF

Question

A. 6(8y+6x)
B. 12(4y+3z)
C. 4(12y+9z)
D. 16(3y+2x)

Answer 1

To factor the expression \( 48y + 36z \) using its greatest common factor (GCF):

1. Identify the coefficients: The coefficients are 48 and 36.

2. Find the GCF of these coefficients:

   • The prime factorization of 48 is \( 2^4 \times 3 \).
   • The prime factorization of 36 is \( 2^2 \times 3^2 \).
   • The GCF is found by taking the lowest power of each common prime factor:
     • For 2, the minimum power is \( 2^2 = 4 \).
     • For 3, the minimum power is \( 3^1 = 3 \).
   • Therefore, the GCF of 48 and 36 is \( 4 \times 3 = 12 \).

3. Factor out the GCF from the expression: \[ 48y + 36z = 12(4y + 3z) \]

Thus, the expression can be factored as \( 12(4y + 3z) \).

The correct answer is B. 12(4y + 3z).