What is the Greatest Common Factor (GCF)?
The largest number that will divide evenly into each of a group of numbers
The Greatest Common Factor (GCF) is the biggest number that divides evenly into two or more numbers. It’s called “common” because it divides evenly into all the numbers in the group, and “greatest” because it’s the largest one that does so.
For example, the GCF of 12 and 18 is 6, because 6 is the biggest number that divides evenly into both 12 and 18.
We use the GCF when:
- Simplifying fractions (e.g., 12/18 simplifies to 2/3 using the GCF)
- Solving problems with equal groupings
- Finding patterns and common structures in numbers
- Factoring expressions and equations
When Do Students Learn About the Greatest Common Factor?
Students are introduced to the idea of common factors as part of their work with multiplication, division, and fractions.
Grades 4–5 – Introduction to Factors and GCF
Students learn to list factors of numbers and identify the GCF of small number pairs.
Grades 6+ – Applying GCF in Math Problems
Students apply the GCF when simplifying fractions, solving ratio problems, and exploring number relationships in algebra.
