<*mathematics*> (GCD) A function that returns the largest
positive integer that both arguments are integer multiples
of.
See also Euclid's Algorithm. Compare: {lowest common
multiple}.
(1999-11-02)

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted \gcd (x,y).

¦ noun the highest number that can be divided exactly into each of two or more numbers.

Greatest common divisor

In mathematics, the **greatest common divisor** (**GCD**) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers *x*, *y*, the greatest common divisor of *x* and *y* is denoted $\gcd(x,y)$. For example, the GCD of 8 and 12 is 4, that is, $\gcd(8,12)=4$.

In the name "greatest common divisor", the adjective "greatest" may be replaced by "highest", and the word "divisor" may be replaced by "factor", so that other names include **highest common factor** (**hcf**), etc. Historically, other names for the same concept have included **greatest common measure**.

This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see § In commutative rings below).

Pronunciation examples for Greatest common divisor

1. literally, it's like November 6th, 2006. It was greatest common divisor, least common