Show that if $x^d -1$ divides $x^n -1$ if and only if $d$ divides $n$

Question

I have done one part. If $d$ divides $n$ then $n=dp$ for some $p$ in $\mathbb{Z}$. Then $x^n -1=x^{dp} -1$. Then $x^d -1$ is a factor of $x^n-1$. So $x^d -1$ divides $x^n -1$.

But how to show reverse part?