Find the greatest common divisor of two whole numbers.
Try an example
Load a ready-made sample into this tool and run it. Every result you see is calculated live by the tool itself — nothing here is a pre-written answer.
Sample: a: 48; b: 36
How to Use
- Enter two whole numbers.
- Click Run.
- Read the largest number that divides both.
What this GCD calculator does
This GCD calculator finds the greatest common divisor of two whole numbers — the largest number that divides both of them exactly, with nothing left over. Enter the pair and it returns the GCD straight away. The result is the key step behind simplifying fractions, reducing ratios to lowest terms and splitting quantities into the largest possible equal groups. No factor lists for either number need to be written out by hand.
How the GCD is found
The standard method is Euclid’s algorithm: divide the larger number by the smaller, keep the remainder, then repeat using the divisor and the remainder until the remainder reaches zero. The last divisor used is the GCD. It reaches the answer in very few steps even for large numbers, where listing every factor of both would take far longer.
Good to know
Only whole numbers are accepted, and the calculator works with one pair at a time — for three or more numbers, find the GCD of the first two, then the GCD of that result and the next number. A zero entered beside another number returns that number itself, since every number divides zero.
Frequently asked questions
What is the GCD used for?
Most often, simplifying fractions and ratios: dividing both parts by the GCD gives lowest terms in one step. It also finds the largest equal group size dividing two quantities without remainder.
Is GCD the same as HCF?
Yes — greatest common divisor and highest common factor are two names for the same value, GCD in American texts and HCF in British ones. The calculator returns that value either way.
Can I find the GCD of three numbers?
The calculator takes two numbers at a time. For three, find the GCD of any two, then the GCD of that answer and the third number — the divisor common to all three.
How to use GCD Calculator
- Enter two whole numbers.
- Click Run.
- Read the largest number that divides both.
Limitations
Only whole numbers are accepted; zero pairs with any number to give that number itself.