GCF Calculator
Find the greatest common factor of two or more numbers, with factors, prime factorization and step-by-step work. Free and instant.
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About the GCF Calculator
The greatest common factor (GCF), also called the greatest common divisor (GCD) or highest common factor (HCF), is the largest whole number that divides all the numbers exactly. This calculator accepts two or more numbers, shows each prime factorization, and for two numbers also shows the Euclidean algorithm steps.
You can also use it to simplify fractions: divide the numerator and denominator by their GCF. For the least common multiple, see the LCM calculator.
How to use it
- Type two or more positive whole numbers, separated by commas or spaces.
- Press Find GCF.
- Read the GCF, the prime factorization of each number and the Euclid steps.
How to find the GCF
- Prime factorization: write each number as a product of primes, then multiply the primes they share (using the lowest power).
- Euclid’s algorithm: divide the larger number by the smaller, replace the larger by the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF.
- Listing factors: list all factors of each number and pick the biggest one they have in common.
Example: GCF(48, 180). 48 = 24 × 3 and 180 = 22 × 32 × 5, so GCF = 22 × 3 = 12.
GCF examples
| Numbers | GCF |
|---|---|
| 12 and 18 | 6 |
| 24 and 36 | 12 |
| 48 and 180 | 12 |
| 100 and 75 | 25 |
| 17 and 31 | 1 (coprime) |
| 36, 60 and 84 | 12 |
Frequently asked questions
What is the GCF of two numbers?
The largest whole number that divides both numbers with no remainder. For 12 and 18 it is 6.
Is GCF the same as GCD or HCF?
Yes. GCF, GCD (greatest common divisor) and HCF (highest common factor) are three names for the same value.
How do I use the GCF to simplify a fraction?
Divide the numerator and denominator by their GCF. For 18/24 the GCF is 6, so the fraction simplifies to 3/4.
What is the GCF of a number and 1?
It is always 1, because 1 is the only common factor.
What if the GCF is 1?
Then the numbers are coprime (relatively prime): they share no common factor other than 1.
Last reviewed: November 2026.
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