Non-Zero Integer has Finite Number of Divisors

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Let $n \in \Z_{\ne 0}$ be a non-zero integer.

Then $n$ has a finite number of divisors.


Let $S$ be the set of all divisors of $n$.

Then from Absolute Value of Integer is not less than Divisors:

$\forall m \in S: -n \le m \le n$

Thus $S$ is finite.