Largest divisor shared by the entire set of numbers. Aka: greatest common factor, highest common factor. Enter your numbers, separate by a comma.
The greatest common divisor (gcd/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 number is known by a few other names: the greatest common factor (gcf), greatest common denominator, highest common factor (hcf), or greatest common measure.
This calculator is based on Euclid's algorithm, an efficient method for computing the greatest common divisor (GCD) 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.
The Euclidean algorithm is 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. The same concept was independently discovered at a later date by both Indian and Chinese mathematicians.