7th grade factoring out the greatest common factor worksheets
Factoring writes a sum or difference as a product. On this sheet, students factor out the greatest positive integer common factor from a variable term and a constant. Each of the eight problems has a worked answer and an expansion check. Easier uses smaller numbers and mostly positive terms. On level mixes all four sign patterns. Harder uses more negative terms and GCFs smaller than the absolute value of either coefficient. Every harder sheet includes GCFs of 4 and 6, where taking out a smaller common factor leaves more work to do.
Free printable PDF worksheet, aligned to Common Core 7.EE.A.1.
Each print is a different sheet with its own answer key. You don't need to sign up.
Need one more? These are the skills next door at this grade.
The kind of problems you'll get
Factor out the greatest positive integer common factor. Show your steps, then expand to check.
-
4 × z + 12
Answer: 4 × (z + 3)
-
20 × n + 5
Answer: 5 × (4 × n + 1)
-
12 × p − 6
Answer: 6 × (2 × p − 1)
Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.
What's on a 7th grade sheet
- Factoring out the greatest common factor. Factor out the greatest positive integer common factor. Show your steps, then expand to check. 8 problems per page.
Every version prints on US Letter or A4, with its answer key after the problems.
How to teach this
Find the GCF using the magnitudes of the two coefficients. Divide each term by that positive number and keep its sign inside the parentheses. The two numbers left inside should have no common integer factor greater than 1.
Watch for: Use the greatest common factor, not just any common factor. Keep the sign of each term when dividing by the positive GCF.
Common questions about 7th grade factoring out the greatest common factor
- Should students factor out a negative number?
- This sheet asks for the greatest positive integer common factor. Negative terms keep their signs inside the parentheses.
- How can students check their answers?
- Distribute the outside factor. The expanded expression should match the original expression.
- What is included in the answer key?
- By default, the key shows the GCF, the division of each term, the final factorization, and an expansion check. Choose Answers only for final answers without the worked steps.
Related worksheets
- 7th grade adding linear expressions Same grade, nearby skill
- 7th grade checking contextual solutions Same grade, nearby skill
- 7th grade collecting rational like terms Same grade, nearby skill
- 7th grade collecting terms and constants Same grade, nearby skill
- Factoring out the greatest common factor, all grades The full progression
- All 7th grade math worksheets Every skill at this level
- All 7th grade worksheets Everything at this level
Ready to print one?
Need a fresh set of problems? Print another copy. The difficulty you picked above stays.
Aligned to Common Core 7.EE.A.1. Reviewed by the One more sheet team. Content version 241, updated October 2026.
Spot a mistake on this sheet? Tell us. · About these worksheets