Let $n$, $m\in\N$. $n$ divides $m$, written
\[n\divides m,\]if there exists $k\in\N$ such that
\[m = kn.\]
- Instead of “$n$ divides $m$”, we also say
- $n$ is a divisor / factor of $m$;
- $m$ is a multiple of $n$;
- $m$ is divisible by $n$.
For all $n\in\N$,
\[0 \divides n.\]For all $n\in\N^+$,
\[n \ndivides 0.\]