## The Lesson

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

## What's in a Name?

The Greatest Common Factor (GCF) is so called because it is the largest (*greatest*) factor that is the same (

*common*) to the numbers. It may sometimes be called:

- Greatest Common Divisor (GCD)
- Highest Common Factor (HCF)