Question

Factor 48y+36z
using the GCF.(1 point)
Responses

12(4y+3z)
12 left parenthesis 4 y plus 3 z right parenthesis

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

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

16(3y+2z)

Answer 1

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

1. **Find the GCF of 48 and 36**:
- The factors of 48 are: \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \)
- The factors of 36 are: \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \)
- The common factors are: \( 1, 2, 3, 4, 6, 12 \)
- The greatest common factor is **12**.

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

Thus, the expression factored using the GCF is:
\[
\boxed{12(4y + 3z)}
\]