Factoring GCF Worksheet

This factoring GCF worksheet helps students practice identifying the greatest common factor and rewriting expressions in factored form. The printable set includes 12 randomized questions and an answer key on page 2.

What is Factoring GCF?

Factoring GCF means finding the greatest common factor shared by all the terms in an expression and pulling it outside parentheses. This is often the first step in simplifying or factoring more complicated polynomials.

How to Factor Out the GCF

1. Find the greatest common numerical factor in all terms.
2. Check whether the variable part also has a common factor.
3. Divide each term by the GCF.
4. Write the expression as the GCF times the simplified parentheses.

Example

Factor $6x^2 + 12x$

The greatest common factor is $6x$.

So:

$6x^2 + 12x = 6x(x + 2)$

FAQ

Q: Why do we factor out the GCF first?
A: Factoring out the GCF makes the remaining expression simpler and often reveals another factoring step.

Q: Can the GCF include variables?
A: Yes. If every term contains the same variable factor, it should be part of the GCF.