Greatest Common Divisor
Find the largest whole number that divides evenly into every number in your list. This is also called the greatest common factor (GCF) or highest common factor (HCF). It helps reduce fractions and split items into equal groups.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
48, 180, 240
12
How to use the greatest common divisor
- Type 2 to 100 whole numbers in the box, such as 48, 180, 240.
- Separate them with commas, spaces, semicolons or new lines.
- Press Run to see the greatest common divisor.
- Press Copy result or Download to keep it.
How it works
The tool uses the Euclidean algorithm. It keeps replacing the larger number with the remainder after dividing by the smaller one, until the remainder is 0.
Each number can have up to 100 digits, and the math uses exact big integers.
Negative numbers are allowed and treated by their size, so the GCD of -12 and 18 is 6.
Zeros are allowed. If every number is 0, the result is 0 with a note explaining that convention.
Decimals and fractions are rejected, because the GCD is defined for whole numbers.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
How do you find the greatest common divisor?
One way is to list the prime factors of each number and multiply the ones they share. For 48 and 180, the shared factors are 2 × 2 × 3, so the GCD is 12.
Is GCD the same as GCF?
Yes. Greatest common divisor, greatest common factor and highest common factor all mean the same thing.
What is the GCD of 48, 180 and 240?
It is 12, the largest number that divides all three evenly.
How does the GCD simplify a fraction?
Divide the top and bottom by their GCD. For 48/180, dividing both by 12 gives 4/15.