Greatest common factor (GCF)

Property The greatest common factor (GCF) is the product of the greatest integer and the greatest power of each variable that divides without a remainder into each term.

Examples For $6a^2b^3 + 8a^4b^2c$, the GCF is $2a^2b^2$. For $8c^3d^2e$ and $12c^2d^4e^2$, the GCF is $4c^2d^2e$.

Explanation Basically, the GCF is the biggest, beefiest monomial that fits perfectly into every term. To find it, break each term down to its prime factors, identify all the common parts, and multiply them together.