if $n>0$ and $r>0$ ($n$ and $r$ and positive integers) and $r$ divides $n$ , then $n/r$ divides $nCr$ . Is this statement true?

Using factorial form, it is rather easy to prove (I let you prove this part) that $$\binom{n}{r}=\frac{n}{r}\binom{n-1}{r-1}$$

Therefore if $r$ divides $n$, then yes, $\frac{n}{r}$ divides $\binom{n}{r}$.