Answer
Let $a, b, c$ be integers, where $a\neq 0$. Then if $a|b$ and $b|c$, $a|c$.
Work Step by Step
Let $a, b, c\in \mathbb{Z}$ with $a\neq 0$, and let $a|b$ and $b|c$. Because $b$ is a factor of $c$, we can express $c$ as the product of $b$ and some integer $d$. That is, $c=d\cdot b$. Because $a$ is a factor of $b$, we can express $b$ as the product of $a$ and an integer $g$. Thus, $c=d\cdot b=d\cdot (g\cdot a)=(d\cdot g)\cdot a$. Because the product of the integers $d$ and $g$ is an integer, $a|c$ and the statement above is proved.
