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greatest common factor

The largest monomial that divides every term of an expression.

The greatest common factor (GCF) of a polynomial's terms is the largest monomial that divides each of them evenly. Factoring out the GCF is always the first step of the factoring toolkit.

Examples

$6x^3+9x^2 = 3x^2(2x+3)$ — the GCF is $3x^2$ .