Factoring Out the GCF
Pull the greatest common factor out of every term.
About this topic
Factoring is the reverse of multiplying, and the first step is always to look for a greatest common factor shared by every term. In 6x³ + 9x² the GCF is 3x², so it factors as 3x²(2x + 3). Check by distributing back.
Pulling out the GCF makes the remaining expression simpler and often reveals further factoring. To find it, take the largest number that divides all coefficients and the lowest power of each variable that appears in every term. For 12a²b − 18ab² the GCF is 6ab, giving 6ab(2a − 3b). If the leading term is negative, it is often neater to factor out the negative too.
Factoring is the key to solving equations: once an expression is a product, you can set each part to zero. It also simplifies fractions, as in (4x + 8)/(x + 2) = 4(x + 2)/(x + 2) = 4. It is used to rewrite formulas, like factoring the principal out of P + Prt to get P(1 + rt).
A frequent slip is leaving behind a 1 when a term is entirely the GCF: 5x + 5 becomes 5(x + 1), not 5(x). Always multiply back to verify your answer.
Key ideas
- Find the GCF of coefficients and variables
- Divide each term by it
- Check by distributing
Quick check
Use cases: where Factoring Out the GCF helps
- Homework: review the key idea behind Factoring Out the GCF before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Factoring Out the GCF without notes.
- Visual learning: play with the interactive lab to see how Factoring Out the GCF changes when you adjust its inputs.
- Teaching a friend: explain Factoring Out the GCF in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Factoring Out the GCF?
Pull the greatest common factor out of every term.
What will I learn in Factoring Out the GCF?
Find the GCF of coefficients and variables. Divide each term by it. Check by distributing.
Is Factoring Out the GCF part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Factoring Out the GCF lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Factoring Out the GCF?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.