GCF Calculator
Find the GCF, GCD, or HCF of two or more whole numbers. See prime factorizations and Euclidean algorithm steps instantly.
Want to learn more? Browse our calculation guides and tutorials →
Find the GCF, GCD, or HCF of two or more whole numbers. See prime factorizations and Euclidean algorithm steps instantly.
Want to learn more? Browse our calculation guides and tutorials →
Find the greatest common factor of two or more integers with prime factorization and Euclidean algorithm steps.
Enter two or more integers. Commas and spaces are accepted.
Enter values above to see results.
Want to learn more? Browse our calculation guides and tutorials →
The GCF (also called GCD or HCF) is the largest positive whole number that divides every input exactly. For 24, 36, and 60, the GCF is 12.
| Method | Best for | Core idea |
|---|---|---|
| Factor lists | Small numbers | Choose the largest shared factor |
| Prime factorization | Showing why | Multiply shared primes at their lowest powers |
| Euclidean algorithm | Large numbers | Repeat GCF(a,b) = GCF(b,a mod b) |
48 = 2⁴ × 3 and 18 = 2 × 3². Their shared primes at the lowest powers are 2 × 3, so the GCF is 6. With Euclid: 48 mod 18 = 12, 18 mod 12 = 6, and 12 mod 6 = 0.
The greatest common factor is the largest positive integer that divides every given integer without a remainder.
Yes. Greatest common factor, greatest common divisor, and highest common factor name the same value.
Yes. Find the GCF of the first pair, then find the GCF of that result and each remaining number.
It is 1. Numbers whose only shared positive factor is 1 are called coprime or relatively prime.
The GCF of 0 and n is the absolute value of n because every nonzero integer divides 0.