Definition:Common Divisor

Let $$S$$ be a finite set of integers, that is:

$$S = \left\{{x_1, x_2, \ldots, x_n: \forall k \in \mathbb{N}^*_n: x_k \in \mathbb{Z}}\right\}$$.

Let $$c \in \mathbb{Z}$$ such that $$c$$ divides all the elements of $$S$$, that is:

$$\forall x \in S: c \backslash x$$.

Then $$c$$ is a common divisor (or "common factor") of all the elements in $$S$$.