Definition:Common Divisor/Real Numbers

Definition
Let $S$ be a finite set of real numbers, that is:


 * $S = \set {x_1, x_2, \ldots, x_n: \forall k \in \N^*_n: x_k \in \R}$

Let $c \in \R$ such that $c$ divides all the elements of $S$, that is:


 * $\forall x \in S: c \divides x$

Then $c$ is a common divisor of all the elements in $S$.

Also known as
The term common factor is also often found, meaning the same thing as common divisor.

In 's, the term common measure is universally used for this concept.