Greatest Common Factor (GCF)
Practise finding the greatest common factor of two numbers — the key to simplifying fractions.
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How to find the GCF
The greatest common factor of two numbers is the largest number that divides both. It’s the tool you use to simplify fractions in one step.
- List the factors of each number (or its prime factors).
- Find the factors they share.
- The biggest shared factor is the GCF.
For example, 12 = 2×2×3 and 18 = 2×3×3 share a 2 and a 3, so the GCF is 2×3 = 6.
Worked examples
Tips & common mistakes
For small numbers, listing factors is fine; for bigger ones, prime factorisation is faster and surer. The divisibility rules speed up the hunt for shared factors. Type the GCF.
- Giving a common factor that isn’t the greatest one (saying 2 for 12 and 18 instead of 6).
- Listing a factor of only one of the numbers.
- Confusing GCF (a factor, so smaller) with LCM (a multiple, so bigger).
Frequently asked questions
What is the greatest common factor?
The largest number that divides both numbers exactly. The GCF of 12 and 18 is 6.
How do I find the GCF?
List the factors of each number and pick the largest they share, or use prime factorisation and multiply the common primes.
What is the GCF used for?
Mainly simplifying fractions — dividing the top and bottom by their GCF reduces a fraction in one step.
How is GCF different from LCM?
GCF is the largest factor two numbers share (smaller than them); LCM is the smallest multiple they share (larger than them).
What grade is this?
Greatest common factor is a grade 5–6 skill.