justyourcalculatorGreatest Common Factor Calculator
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GCF Calculator
Greatest common factor, with Euclid's steps
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GCF(48, 180, 300)
12
- Relatively prime?
- No
How it was calculated
- Euclid's algorithm: replace (a, b) with (b, a mod b) until the remainder is 0.
- 180 = 3 × 48 + 36
- 48 = 1 × 36 + 12
- 36 = 3 × 12 + 0
- GCF so far = 12
- 300 = 25 × 12 + 0
- GCF so far = 12
- 48 = 2⁴ × 3
- 180 = 2² × 3² × 5
- 300 = 2² × 3 × 5²
- Common primes at their lowest power: 2² × 3 = 12
- All common factors (the factors of 12): 1, 2, 3, 4, 6, 12
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How the gcf calculator works
The greatest common factor (GCF), also called the greatest common divisor (GCD) or highest common factor (HCF), is the largest whole number that divides every number in the set with no remainder.
Euclid's algorithm finds it fast: divide the larger number by the smaller, keep the remainder, and repeat with the smaller number and the remainder until the remainder is 0. The last nonzero remainder is the GCF. The prime factor method multiplies the primes all the numbers share, at their lowest power.
The GCF is what you divide by to simplify a fraction or ratio to lowest terms.
Using and checking your result
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