Image: Wikimedia Commons

Euclidean algorithm

Algorithm for computing greatest common divisors

Also known as Euclid's algorithm · GCD algorithm

Instance of: algorithm

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his Elements . It is an example of an algorithm, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations.

Overview

All data

24 statements · 8% with external sources · numbers in brackets are citations

Named after: Euclid

On other databases

23 identifiers linking Euclidean algorithm across the web's reference databases

Data quality

statements

externally sourced

Source last edited July 26, 2026. AIDb refreshes this page daily.

Suggest a fact or correction

Links

Use this data

curl https://aidb.si/api/v1/entities/Q230848

API docs, limits & keys

Cite this page

AIDb. (2026). Euclidean algorithm (Q230848). Retrieved from https://aidb.si/e/euclidean-algorithm-Q230848