Divisor is Reciprocal of Divisor of Integer

Theorem
Let $a, b, c \in \Z_{>0}$.

Then:
 * $b = \dfrac 1 c \times a \implies c \divides a$

where $\divides$ denotes divisibilty.

Proof
Let $a$ have an aliquot part $b$.

Let $c$ be an integer called by the same name as the aliquot part $b$.

Then:
 * $1 = \dfrac 1 c \times c$

and so by :
 * $ 1 : c = b : a$

Hence the result.