Find the greatest common factor of two or more numbers.
The GCF is the largest number that divides all your numbers exactly. The GCF of 48, 180 and 60 is 12.
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 a list. Enter two or more whole numbers and the calculator gives the GCF, the LCM, each number's prime factors and the step-by-step Euclidean algorithm.
The GCF is used to simplify fractions and ratios. See the LCM Calculator, Factor Calculator, Common Factor Calculator and Fraction Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| GCF | 12 |
| LCM | 720 |
| Numbers divided by the GCF | 4, 15, 5 |
| Prime factors of 48 | 2⁴ × 3 |
| Prime factors of 180 | 2² × 3² × 5 |
| Prime factors of 60 | 2² × 3 × 5 |
| Division step | Remainder |
|---|---|
| 180 = 3 × 48 + 36 | 36 |
| 48 = 1 × 36 + 12 | 12 |
| 36 = 3 × 12 + 0 | 0 |
| Numbers | GCF |
|---|---|
| 48 and 18 | 6 |
| 48, 180, 60 | 12 |
| 100, 75, 50 | 25 |
| 17 and 5 | 1 |
| 84, 126, 210 | 42 |
The largest whole number that divides each of the numbers without a remainder.
Yes — three names for the same thing, used in different countries and textbooks.
Write each number as a product of primes and multiply the primes they share, using the smallest power of each.
A fast method that repeatedly replaces the pair (a, b) by (b, a mod b) until the remainder is zero.
1. Coprime numbers share no factor other than 1, such as 8 and 15.
To simplify fractions and ratios, to split things into equal groups and in cryptography.
It uses the standard method: gcd(a, b) = gcd(b, a mod b) until the remainder is 0 lcm(a, b) = a × b ÷ gcd(a, b) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
