# What Is the Greatest Common Factor in Algebra?

## What Is the Greatest Common Factor in Algebra?

The greatest common factor in algebra is the largest factor that is common to two or more terms.

## Understanding the Greatest Common Factor in Algebra

A factor is a quantity that divides exactly into a term.

It is one of the numbers, letters and brackets (or a product of them) that are multiplied together to make a term.

For example,

The greatest common factor is the largest collection of numbers and letters that make up both terms.

In our example, **2x** is the greatest common factor.

**2x** is the largest term that divides exactly into both original terms (2xy and 2xz).

**2x**y ÷ **2x** = y

**2x**z ÷ **2x** = z