# How do you find the greatest common factors of variable expressions?

##### 1 Answer

The 'normal' way of finding the GCF of two polynomials is to factor both of them completely, then pick out the common factors and multiply them together.

Alternatively you can use division.

#### Explanation:

**Normal Method - Factor both polynomials first**

For example:

Given

you can factor

hence the GCF is

**Backup Method - Using division of polynomials**

Given:

and:

If

For example,

Let

If we now divide

Next try dividing

This time there is no remainder, so

For a more complex example, see http://socratic.org/questions/if-you-are-told-that-x-7-3x-5-x-4-4x-2-4x-4-0-has-at-least-one-repeated-root-how