The formula
How it works
The greatest common factor (GCF) is the largest whole number that divides evenly into all of your numbers. Enter two or three numbers and the calculator finds their GCF — the key to simplifying fractions and splitting things into equal groups.
FAQ
Is GCF the same as GCD?
Yes. Greatest common factor (GCF), greatest common divisor (GCD) and highest common factor (HCF) are three names for exactly the same thing.
What if the numbers share no factors?
Then their GCF is 1, and they are called “coprime” or relatively prime. For example 8 and 9 share no factor other than 1.
How do I find the GCF using prime factorization?
Break each number into its prime factors, then multiply together the primes they have in common, using the lowest power that appears in every number. For 48 (2⁴×3) and 36 (2²×3²), the shared primes give 2²×3 = 12.
How is GCF different from LCM?
The GCF is the largest number that divides evenly into all your numbers, while the least common multiple (LCM) is the smallest number that all of them divide into evenly — they measure opposite ends of the same relationship.
Can I find the GCF of more than three numbers?
Yes, in principle — find the GCF of the first two, then take the GCF of that result with each additional number in turn. This calculator supports up to three at a time, so repeat the process for more.
Why is finding the GCF useful when simplifying fractions?
Dividing both the numerator and denominator by their GCF reduces a fraction to its lowest terms in one step, rather than dividing by smaller common factors repeatedly.
What is the GCF of a number and zero?
The GCF of any number and 0 is that number itself, since every whole number divides evenly into 0. The calculator ignores blank or zero entries so it only compares the numbers you actually provide.
About the greatest common factor calculator
This calculator finds the greatest common factor of two or three whole numbers — the biggest number that divides all of them with no remainder. The GCF is a building block of arithmetic. It is what you use to reduce a fraction to its simplest form, and it answers practical questions like the largest equal group you can split several quantities into. Because it only makes sense for whole numbers, the calculator works with integers.
How to use it
Enter two numbers, or add a third if you need it, and leave the last box at zero to ignore it. The calculator returns their greatest common factor. For example, the GCF of 48 and 36 is 12, because 12 is the largest number that divides both. That is why the fraction 36/48 simplifies to 3/4 — you divide the top and bottom by their GCF. If the answer comes back as 1, the numbers share no common factor.
The formula
The fastest way to find a GCF is the Euclidean algorithm, based on the rule , where is the remainder when is divided by . You keep replacing the pair with the smaller number and the remainder until the remainder is zero; the last non-zero value is the GCF. For three numbers you find the GCF of the first two, then the GCF of that result with the third.
Where it is used
The GCF is used constantly in working with fractions, since simplifying one always means dividing by the greatest common factor. It shows up in tiling and packing problems, where you want the largest equal size that fits several dimensions, and in scheduling and sharing, where quantities must be split into equal whole groups. In cryptography and computing, the closely related Euclidean algorithm is a core tool for working with large numbers efficiently.