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 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). In this article we will denote the greatest common divisor of two integers a and b as gcd(a,b). Some authors use (a,b).