Question

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

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

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)

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

2. **Factoring out the GCF:**
Now we divide each term by the GCF (which is 12):
\[
48y \div 12 = 4y
\]
\[
36z \div 12 = 3z
\]

3. **Writing the factored form:**
Therefore, the expression can be factored as:
\[
48y + 36z = 12(4y + 3z)
\]

So, the correct factored form is:

**12(4y + 3z)**