To factor \( 48y + 36z \) using the greatest common factor (GCF), we first need to find the GCF of the coefficients 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 greatest common factor (GCF) is 12.
Now, we can factor out the GCF from the expression:
\[ 48y + 36z = 12(4y + 3z) \]
Thus, the correct factorization is:
12(4y + 3z).