Factor 48y+36z using the GCF

To factor 48y + 36z using the greatest common factor (GCF), we need to find the largest common number that can divide evenly into both terms.

First, let's find the prime factorization of each term:

48y = 2^4 * 3 * y
36z = 2^2 * 3^2 * z

The GCF is found by taking the lowest exponent for each common prime factor. In this case, the common prime factors are 2 and 3.

The lowest exponent of 2 is 2, and the lowest exponent of 3 is 1.

Therefore, the GCF of 48y and 36z is 2^2 * 3 = 12.

Now, we can factor out the GCF from each term:

48y + 36z = 12 * (4y + 3z)