Absolute Value of Integer is not less than Divisors

Theorem
A (non-zero) integer is greater than or equal to its divisors in magnitude:

$$\forall c \in \mathbb{Z}^*: a \backslash c \Longrightarrow a \le \left|{a}\right| \le \left|{c}\right|$$

It follows that a non-zero integer can have only a finite number of divisors, since they must all be less than or equal to it.

Proof
Suppose $$a \backslash c, c \ne 0$$. It's a given that $$a \le \left|{a}\right|$$.