Definition:Greatest Common Divisor/Integers/General Definition

Definition
Let $S = \set {a_1, a_2, \ldots, a_n} \subseteq \Z$ such that $\exists x \in S: x \ne 0$ (that is, at least one element of $S$ is non-zero).

Definition 2
By convention:
 * $\map \gcd \O = 1$

Also see

 * Equivalence of Definitions of Greatest Common Divisor of Set of Integers


 * Greatest Common Divisor is Associative for a justification of this construction.