What is the Greatest Common Factor of 36x+12y

12 because 12 divides into both 36 and 12

If you were asked to factor,the answer would be:
12(3x+y)

To find the Greatest Common Factor (GCF) of 36x and 12y, we need to determine the largest number or algebraic expression that can divide both terms evenly.

Step 1: Determine the factors of each term:
The factors of 36x are: 1, 2, 3, 4, 6, 9, 12, 18, 36, x, 2x, 3x, 4x, 6x, 9x, 12x, 18x, and 36x.

The factors of 12y are: 1, 2, 3, 4, 6, 12, y, 2y, 3y, 4y, 6y, and 12y.

Step 2: Identify the common factors:
The common factors of 36x and 12y are: 1, 2, 3, 4, 6, and 12.

Step 3: Determine the Greatest Common Factor (GCF):
The largest common factor shared by both terms is 12. Therefore, the Greatest Common Factor (GCF) of 36x and 12y is 12.

So, the GCF of 36x and 12y is 12.