How to use the GCF calculator
Type 2 to 10 whole numbers separated by commas or spaces and press Find GCF. You see the factors listed, the prime factors and – for two numbers – Euclid's method, so you can follow whichever your class uses.
What is the greatest common factor?
The greatest common factor (GCF) – also called the greatest common divisor (GCD) or highest common factor (HCF) – is the biggest number that divides every number in the list exactly. It is used to simplify fractions and to split things into equal groups.
Three ways to find the GCF
- List the factors and pick the greatest one they share. Factors of 12: 1, 2, 3, 4, 6, 12; of 18: 1, 2, 3, 6, 9, 18 → GCF 6.
- Prime factors: multiply the primes they share, each with its lowest power. 12 = 2² × 3, 18 = 2 × 3² → GCF = 2 × 3 = 6.
- Euclid's method: 18 = 1 × 12 + 6, then 12 = 2 × 6 + 0. The last non-zero remainder, 6, is the GCF.
Numbers whose GCF is 1 are called coprime (relatively prime), like 8 and 15.
Frequently asked questions
What is the GCF of 12 and 18?
6. It is the largest number that divides both 12 and 18.
Is GCF the same as GCD and HCF?
Yes. Greatest common factor, greatest common divisor and highest common factor all mean the same thing.
How do you find the GCF of three numbers?
Find the factors (or prime factors) all three share, or work in pairs: GCF(a, b, c) = GCF(GCF(a, b), c).
What does a GCF of 1 mean?
The numbers share no factor except 1 – they are coprime.
How is the GCF used with fractions?
Divide the numerator and denominator by their GCF to simplify a fraction in one step: 18/24 ÷ 6 = 3/4.