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Euclid’s Algorithm

In mathematics, the Euclidean algorithm, or Euclid’s algorithm, is a method for computing the greatest common divisor (GCD) of two (usually positive) integers, also known as the greatest common factor (GCF) or highest common factor (HCF). It is named after the Greek mathematician Euclid, who described it in Books VII and X of his Elements.

Euclid’s method for finding the greatest common divisor (GCD) of two starting lengths BA and DC, both defined to be multiples of a common “unit” length. The length DC being shorter, it is used to “measure” BA, but only once because remainder EA is less than CD. EA now measures (twice) the shorter length DC, with remainder FC shorter than EA. Then FC measures (three times) length EA. Because there is no remainder, the process ends with FC being the GCD.

Here are two examples of Euclid’s Algorithm written in pseudocode:

A recursive implementation:

Credit: Wolfram Alpha/Wikipedia