 The notion of greatest common divisor can more generally be defined for elements of an arbitrary commutative ring, although in general there need not exist one for every pair of elements.If is a commutative ring, and and are in , then an element of is called a "common divisor" of and if it divides both and (that is, if there are elements and in such that "d"·"x" = "a" and "d"·"y" = "b").If is a common divisor of and , and every common divisor of and divides , then is called a "greatest common divisor" of and "b".