Find the greatest common factor of two or more whole numbers, see all their common factors, and follow the Euclidean algorithm and prime-factor methods step by step.
GCF = 22 × 3 = 12
How to use the GCF calculator
Type two or more positive whole numbers separated by commas or spaces. The calculator returns the greatest common factor, lists every common factor, shows each number divided by the GCF (handy for simplifying fractions and ratios) and gives the least common multiple as a bonus. The steps walk through the Euclidean algorithm and confirm the answer with prime factorization.
The greatest common factor goes by several names: GCF (greatest common factor), GCD (greatest common divisor) and HCF (highest common factor, the usual term in the UK and India). They all mean the largest whole number that divides every number in the set without a remainder.
Three ways to find the GCF
1. List the factors
Write out all the factors of each number and pick the largest one they share. For 24 and 36: factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors are 1, 2, 3, 4, 6 and 12, so the GCF is 12. This works well for small numbers but quickly becomes tedious.
2. Prime factorization
Break each number into primes and multiply the primes they all have in common, using the lowest power that appears:
GCF = 22 × 3 = 12
The prime factorization calculator breaks down any number for you.
3. The Euclidean algorithm
The fastest method, and the one computers use, relies on the fact that GCF(a, b) = GCF(b, a mod b). Repeatedly divide the larger number by the smaller and replace the larger with the remainder until the remainder is zero. The last non-zero remainder is the GCF.
Worked example: GCF of 24, 36 and 60
- GCF(36, 24): 36 = 1 × 24 + 12; 24 = 2 × 12 + 0. The last non-zero remainder is 12.
- GCF(60, 12): 60 = 5 × 12 + 0, so the GCF is 12.
- Therefore GCF(24, 36, 60) = 12. The common factors are 1, 2, 3, 4, 6 and 12.
Dividing each number by 12 gives 2, 3 and 5 — which have no common factor left, confirming 12 is the greatest.
Where the GCF is used
- Simplifying fractions: divide the numerator and denominator by their GCF. 24/36 ÷ 12/12 = 2/3. The fraction calculator does this automatically.
- Simplifying ratios: 24 : 36 : 60 simplifies to 2 : 3 : 5. See the ratio calculator.
- Dividing things into equal groups: if you have 24 apples, 36 oranges and 60 bananas and want identical gift baskets with no fruit left over, the most baskets you can make is the GCF, 12 — each with 2 apples, 3 oranges and 5 bananas.
- Tiling and cutting: the largest square tile that exactly covers a 240 cm × 360 cm floor has a side equal to GCF(240, 360) = 120 cm.
- Factoring algebra: pulling out the GCF is the first step in factoring expressions like 24x + 36y = 12(2x + 3y).
GCF and LCM
For two numbers, the GCF and the least common multiple are linked by a neat identity: GCF(a, b) × LCM(a, b) = a × b. For 24 and 36: 12 × 72 = 864 = 24 × 36. If you need the smallest number that all your numbers divide into — for adding fractions, for example — use the LCM calculator.
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Calcivia. (2026). GCF Calculator. Retrieved October 31, 2026, from https://www.calcivia.com/gcf-calculator/"GCF Calculator." Calcivia, 2026, https://www.calcivia.com/gcf-calculator/. Accessed 31 Oct. 2026.<a href="https://www.calcivia.com/gcf-calculator/">GCF Calculator</a> by Calcivia