01 Key Concepts
Definition
The GCF of two or more numbers is the largest number that is a factor of all of them.
Finding GCF by Listing Factors
List all factors of each number, then pick the largest one they have in common.
Finding GCF by Prime Factorization
Break each number into prime factors, then multiply together the lowest power of each prime shared by all numbers.
Using GCF to Simplify Fractions
Divide both the numerator and denominator of a fraction by their GCF to reduce it to lowest terms.
GCF of More Than Two Numbers
The same methods extend naturally — find the largest factor shared by every number in the group.
02 Solved Examples
Example 1 Find the GCF of 12 and 18.
- Factors of 12: 1,2,3,4,6,12.
- Factors of 18: 1,2,3,6,9,18.
- The largest common factor is 6.
Answer: GCF(12,18) = 6
Example 2 Find the GCF of 24 and 36 using prime factorization.
- 24 = 2^3 * 3.
- 36 = 2^2 * 3^2.
- Take the lowest power of each shared prime: 2^2 * 3^1 = 4*3.
Answer: GCF(24,36) = 12
Example 3 Simplify the fraction 16/24 using the GCF.
- Find GCF(16,24): factors of 16 are 1,2,4,8,16; factors of 24 are 1,2,3,4,6,8,12,24; GCF=8.
- Divide both parts by 8: 16/8=2, 24/8=3.
Answer: 16/24 simplifies to 2/3
03 Practice Questions
1Find the GCF of 8 and 12.
4
2Find the GCF of 15 and 25.
5
3Find the GCF of 9 and 27.
9
4Simplify 10/15 using the GCF.
2/3
5Find the GCF of 14 and 21.
7
📄 Greatest Common Factor — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.