If $b$ divides $ck$ and $b$ and $c$ are relatively prime, then $b$ must divides $k$

Question

Suppose $b, c\in\mathbb{Z}$ and the greatest common divisor of $b$ and $c$ is $1$, i.e., $b$ and $c$ are relatively prime. If $b$ divides $ck$ for some positive integer $k$, then $b$ must divide $k$.

Could someone please give a proof for why $b$ must divide $k$?

Answer 1

This result is Gauß's lemma. It generalizes Euclid's lemma...