Absolute Value of Integer is not less than Divisors

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


 * $\forall c \in \Z_{\ne 0}: a \divides c \implies a \le \size a \le \size c$

Proof
Suppose $a \divides c$ for some $c \ne 0$.

From Negative of Absolute Value:
 * $a \le \size a$

Then:

Also see

 * Non-Zero Integer has Finite Number of Divisors: a direct corollary