In the polynomial 6x3y2, 8x2y and 4xyz for
example, x and y appear in all three terms, so they are both part of the GCF. Z
appears in only one term, so do not include it in the GCF.
Use each variable with the lowest exponent it has in the polynomial for the GCF.
In 6x3y2, 8x2y and 4xyz. 1 is the lowest
exponent with x, The lowest exponent of y is 1. This means xy is part of the GCF
for this polynomial.
The coefficients of 6x3y2, 8x2y and 4xyz are
6, 8, and 4. The prime factorizations are 2×3, 2× 2 × 2 and 2× 2,
respectively. Since only 2 is common factor in all, it is the GCF.
Write the GCF of the coefficients before the GCF of the variables to get the complete
GCF for the polynomial.
Therefore, GCF of 6x3y2, 8x2y and 4xyz is 2xy.