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

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

4x4y - 6x3yz + 8x2y2

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, x2 and y1 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 x2y when factoring out the x2y.

After factoring, the example would appear as:

2x2y(2x2 - 3xz + 4y)