a divides bc if and only if 
For all integers $a,b,c$,
$$\;a\mid bc \iff  \frac{a}{\gcd⁡(a,b)}∣c.$$

Can anyone help me in proving above statement?
I thought I'd start with trying to prove  $\Leftarrow.$
$$\frac{a}{\gcd⁡(a,b)}\mid c \Rightarrow$$
I know that $\gcd(a, b) = ax+by = d$  but I am lost as to how to make use of that to proceed from here.

$ a\mid bc \iff a\mid ac,bc\iff a\mid (ac,bc)=(a,b)c\iff a/(a,b)\mid c\ $ by gcd Distributive Law
