Factor Out the Greatest Common Factor

Factor Out the Greatest Common Factor

When you factor out the greatest common factor (GCF), you rewrite an expression as a product. The GCF is the largest factor shared by every term in the expression.

1. Find the GCF

Look at the numbers and variables in each term.

• For coefficients, choose the largest number that divides all terms evenly.
• For variables, take only the letters that appear in every term, using the smallest exponent common to all.

2. Divide each term by the GCF

Once you identify the GCF, divide every term by it. This gives the expression inside the parentheses.

3. Write the factored form

Put the GCF outside parentheses and the quotients inside: GCF × (remaining terms)

Example idea

If every term has a common factor, such as a number and a variable part, both should be included in the factor. If a variable is missing from one term, it cannot be part of the GCF.

Check your work

Multiply the factor outside the parentheses by each term inside. If you get the original expression back, your factoring is correct.

Common mistake to avoid

Do not factor out more than is common to every term. The factor must divide each term exactly.