The GCF Calculator finds the greatest common factor (greatest common divisor) of two or more whole numbers.
GCF = 15
| Greatest common factor | 15 |
| Factors of 330 | 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330 |
| Factors of 75 | 1, 3, 5, 15, 25, 75 |
| Factors of 450 | 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450 |
| Factors of 225 | 1, 3, 5, 9, 15, 25, 45, 75, 225 |
The greatest common factor (GCF), also called greatest common divisor (GCD) or highest common factor (HCF), is the largest number that divides every number in a set without a remainder. The GCF of 330, 75, 450 and 225 is 15.
List factors and pick the largest shared one. Prime factorization: multiply the primes common to all numbers at their lowest powers (3 × 5 = 15 above). The Euclidean algorithm repeatedly replaces the larger number by the remainder: GCF(450, 330) → GCF(330, 120) → GCF(120, 90) → GCF(90, 30) → 30.
Simplifying fractions (330/450 = 11/15 after dividing by 30), splitting items into equal groups, and tiling rectangles with the largest possible square tiles.
What if the GCF is 1? The numbers are coprime.
Can the GCF be larger than the smallest number? No.
Does order matter? No.