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
A common divisor is also known as a common factor.
In Euclid's The Elements, the term common measure is universally used for this concept.
Also see
- Results about common divisors can be found here.
Sources
- 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $2$. Graphs: Paradox