how do you find the greatest common factor with variables in it???

I am going to use the following for the example for all statement below:

4x^{4}y - 6x^{3}yz + 8x^{2}y^{2}

Begin by finding common factors among the constants in front. Looking at the example, the constants 4, 6, & 8 have a common factor of 2.

After finding in common constants, look for common variables. In the example, x and y occur in all three terms. Once the common variables are identified, find the lowest exponent on each. In the example, the lowest exponent on x is 2 and the lowest exponent
on y is 1. Therefore, x^{2} and y^{1} can be factored out (the 1 on y is only written for example and would not appear in the answer).

Just as you would divide each term by 2 when factoring out the 2, you need to divide each term by x^{2}y when factoring out the x^{2}y.

After factoring, the example would appear as:

2x^{2}y(2x^{2} - 3xz + 4y)