Answer
The greatest common factor, abbreviated GCF,
is an expression of the highest degree that divides each term.
(please see step-by-step for an example)
Work Step by Step
The greatest common factor, abbreviated GCF,
is an expression of the highest degree that divides each term of the polynomial.
Find the greatest integer that divides all coefficients.
Find the greatest power of the variable contained in all the terms
The variable part of the greatest common factor always contains the smallest power of a variable that appears in all terms of the polynomial.
Example:
In $4x^{2}y+10x^{2}y^{2}+12x^{3}y^{4},$
$2$ is a factor of all the coefficients,
$x^{2}$ is the smallest power of x that appears in all the terms,
$y$ is the smallest power of y that appears in all the terms,
So, the GCF is $2x^{2}y.$
