Answer
I show the statement to be true.
Work Step by Step
Define $a|bc$, where $a, b, c$ are positive integers and $a\neq 0$. We seek to prove or disprove the conclusion that $a|b$ or $a|c$.
$a|bc$, so $ag=bc$ for some integer $g$. $a=\frac{bc}{g}=b\frac{c}{g}$ by the properties of integers, without loss of generality between $b$ and $c$. Clearly, $a|b$ or $a|c$.
