greatest common divisor

mathematics

Also known as: GCD

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June 29, 2026

Quick Summary

The greatest common divisor (GCD) is the largest integer that divides two or more integers exactly. For example, the GCD of 56 and 12 is 4.12

The Euclidean algorithm is an efficient method for finding the GCD of two numbers. It involves repeatedly dividing the larger number by the smaller number and using the remainder in the next step until the remainder is zero. The last non-zero remainder is the GCD. This algorithm is also useful for simplifying fractions to their lowest terms.2

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$A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”$
arithmetic
Fundamental theory
…of these numbers, called their greatest common divisor (GCD). If the GCD = 1, the numbers are said to be relatively prime. There also exists a smallest positive integer that is a multiple of each of the numbers, called their least common multiple (LCM).
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…of these numbers, called their greatest common divisor (GCD). If the GCD = 1, the numbers are said to be relatively prime. There also exists a smallest positive integer that is a multiple of each of the numbers, called their least common multiple (LCM).
Read More

Euclidean algorithm
…algorithm, procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek mathematician Euclid in his Elements (c. 300 bc). The method is computationally efficient and, with minor modifications, is still used by computers.
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…algorithm, procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek mathematician Euclid in his Elements (c. 300 bc). The method is computationally efficient and, with minor modifications, is still used by computers.
Read More

number theory
Euclid
…a procedure for finding the greatest common divisor of two whole numbers. This fundamental result is now called the Euclidean algorithm in his honour.
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…a procedure for finding the greatest common divisor of two whole numbers. This fundamental result is now called the Euclidean algorithm in his honour.
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