GCD Calculator / GCF Finder

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Finding Greatest Common Divisor

Largest divisor shared by the entire set of numbers. Aka: greatest common factor, highest common factor. Enter your numbers, separate by a comma.

Greatest Common Divisor: 5
Also need least common multiple? Try here.

Tool Overview: GCD Calculator

What is the Greatest Common Divisor?

The greatest common divisor (GCD) of a set of integers (at least one of which is not zero), is the largest positive integer that divides each of the the numbers without a remainder. This GCD calculator is known by a few other names: the greatest common factor finder (gcf finder), greatest common denominator calculator, highest common factor (hcf), or greatest common measure.

How do you find the GCD??

This GCD calculator is based on Euclid's algorithm, an efficient method for computing the greatest common divisor of two numbers. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number.Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal. When that occurs, they are the GCD of the original two numbers. This greatest common divisor calculator is based on this principle.

How do you find the GCD of 3 numbers?

To find the greatest common factor (GCF) between numbers, take each number and calculate its prime factors. Reduce this down to the set of unique common factors and multiple those factors together. The GCD calculator handles this internally.

How do you use the GCD Calculator?

This GCD calculator is easy to use - simply enter your numbers in the box and hit calculator. The greatest common denominator finder will iterate through the numbers and their divisors to get the answer. This is an extended euclidean algorithm calculator which implements the algorithm above.

How long have we known this?

The GCD calculator / gcf finder? I wrote it a few weeks ago. Oh, you mean the Euclidean algorithm? The Euclidean algorithm that this gcd calculator / gcf finder is based on happens to be one of the oldest algorithms in common use. The algorithm was probably not discovered by Euclid, who compiled results from earlier mathematicians in his Elements. Pythagorean mathematicians likely knew of it and possibly even earlier Greek mathematicians. Well before we made our GCF finder. The same concept (behind the gcd calculator) was independently discovered at a later date by both Indian and Chinese mathematicians.

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