What is "greatest common divisor"

n. The '''greatest common divisor''' of a set is the largest positive integer or polynomial that divides each of the numbers in the set without remainder.

n. the largest integer that divides without remainder into a set of integers [syn: greatest common factor, highest common factor]

In mathematics, the greatest common divisor (gcd) of two or more integers, when at least one of them is not zero, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.

The greatest common divisor is also known as the greatest common factor (gcf), highest common factor (hcf), greatest common measure (gcm), or highest common divisor.

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