Factor 48y+36z

Question

using the GCF.(1 point)
Responses

16(3y+2z)
16 left parenthesis 3 y plus 2 z right parenthesis

4(12y+9z)
4 left parenthesis 12 y plus 9 z right parenthesis

6(8y+6z)
6 left parenthesis 8 y plus 6 z right parenthesis

12(4y+3z)

Answer 1

To factor the expression \(48y + 36z\) using the greatest common factor (GCF), we first need to find the GCF of the coefficients 48 and 36.

1. The prime factorization of 48 is \(2^4 \times 3\).
2. The prime factorization of 36 is \(2^2 \times 3^2\).

The GCF is found by taking the lowest power of each prime factor common to both numbers:

• For the prime \(2\), the lowest power is \(2^2\).
• For the prime \(3\), the lowest power is \(3^1\).

Thus, the GCF of 48 and 36 is: \[ 2^2 \times 3^1 = 4 \times 3 = 12. \]

Now, we factor out 12 from the original expression: \[ 48y + 36z = 12(4y + 3z). \]

So, the factored form of the expression is \(12(4y + 3z)\).

Therefore, the correct response is: 12(4y + 3z).