About the GCF calculator
The greatest common factor (GCF), also called the greatest common divisor (GCD) or highest common factor, is the largest whole number that divides every number in your list without a remainder.
Enter two to ten whole numbers. The calculator returns the GCF, tells you whether the numbers are coprime (GCF of 1), shows each number's prime factorization and gives the least common multiple too. For two numbers it also shows the ratio reduced to lowest terms.
The GCF is what you divide by to simplify a fraction: 18/48 reduces to 3/8 because the GCF of 18 and 48 is 6.
Formula
- Euclid: GCF(a, b) = GCF(b, a mod b), until the remainder is 0
- GCF(a, b, c) = GCF(GCF(a, b), c)
- Using primes: take each shared prime at its lowest power
Example
48 = 2⁴ × 3 and 18 = 2 × 3². Shared primes at their lowest powers give 2 × 3 = 6, so GCF(48, 18) = 6.