# Definition:Common Divisor/Real Numbers

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## 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 Euclid's *The Elements*, the term **common measure** is universally used for this concept.

## Sources

- 1993: Richard J. Trudeau:
*Introduction to Graph Theory*... (previous) ... (next): $2$. Graphs: Paradox