Greatest Common Factor Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Greatest Common Factor.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The largest positive integer that divides evenly into two or more given numbers with no remainder.
The biggest 'piece' size that fits evenly into two numbers—like the largest tile that covers both a 12-unit and 18-unit floor.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: GCF finds the largest common building block shared by numbers.
Common stuck point: Using prime factorization: GCF uses the smaller power of each common prime.
Sense of Study hint: Write the prime factorization of both numbers, then circle the primes they share. Multiply the shared primes using the smaller exponent of each.
Worked Examples
Example 1
easySolution
- 1 Prime-factor each number: 48 = 2^4 \times 3 and 36 = 2^2 \times 3^2.
- 2 Identify the common prime factors and keep the smaller exponent for each: 2^2 and 3^1.
- 3 Multiply those shared factors: 2^2 \times 3 = 4 \times 3 = 12, so the GCF is 12.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
easyRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.