Pre-Algebra · Quick Reference

Greatest Common Factor Cheat Sheet

Pre-Algebra · Lesson 9/10

In one line: the greatest common factor (GCF) is the largest number that divides two or more numbers exactly — a key tool for simplifying fractions.

Key Ideas

1Definition. The GCF of two or more numbers is the largest number that is a factor of all of them.

2Finding GCF by Listing Factors. List all factors of each number, then pick the largest one they have in common.

3Finding GCF by Prime Factorization. Break each number into prime factors, then multiply together the lowest power of each prime shared by all numbers.

4Using GCF to Simplify Fractions. Divide both the numerator and denominator of a fraction by their GCF to reduce it to lowest terms.

5GCF of More Than Two Numbers. The same methods extend naturally — find the largest factor shared by every number in the group.

Worked Examples

Find the GCF of 12 and 18.

GCF(12,18) = 6

Find the GCF of 24 and 36 using prime factorization.

GCF(24,36) = 12

Simplify the fraction 16/24 using the GCF.

16/24 simplifies to 2/3

Practice Yourself

Find the GCF of 8 and 12.

Find the GCF of 15 and 25.

Find the GCF of 9 and 27.

Simplify 10/15 using the GCF.

2/3