Let $a,b,c \in\mathbb Z$ where $a \neq0$ or $b \neq 0$. Suppose that $c \neq 0$ and is a common divisor of $a$ and $b$.

Prove that:

${gcd(a,b)\over |c|}= gcd ({a \over c}, {b \over c})$

What I have so far is

Let $a,b \in \mathbb Z$ , both not zero. If $d = gcd(a,b)$, then $gcd({a \over d},{b \over d})=1$.

But I am not sure how I can use this in the equation we have to prove. Can anyone help please?