GCF Calculator
Find the greatest common factor of two or more numbers.
Try an example
12
About this calculator
How This GCF Calculator Works
Enter two or more numbers, and the calculator returns their greatest common factor — the largest number that divides evenly into every one of them.
Worked Example
The GCF of 24 and 36 is 12 — the largest number that divides evenly into both.
Where GCF Comes Up
GCF (also called the greatest common divisor, or GCD) is most often used to simplify fractions and ratios to their lowest terms — dividing both the numerator and denominator by their GCF. It's also useful for problems like dividing items into equal groups with nothing left over, such as tiling a floor with the largest possible square tiles.
Worked example
The greatest common factor of 24 and 36 is 12 — the largest number that divides both evenly (24 ÷ 12 = 2, 36 ÷ 12 = 3).
Frequently asked questions
How is the GCF calculated?
This calculator uses the Euclidean algorithm, repeatedly dividing and taking remainders until it reaches the largest number that divides every input with no remainder.
What's the GCF used for?
Simplifying fractions to lowest terms, splitting quantities into equal groups, and factoring expressions in algebra all rely on finding the GCF.
What if the numbers share no common factor besides 1?
Then the GCF is 1, and the numbers are called "coprime" — for example, 8 and 15 have a GCF of 1.
Can I find the GCF of more than two numbers?
Yes — add as many numbers as you need; the calculator finds the GCF pairwise across the whole list.