Digit‑rearrangement difference

Let $N$ be a number written in base $r$. Form a new number $N^{\prime }$ by permuting the digits of $N$ in any order. Show that $N-N^{\prime }$ is always divisible by $r-1$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VII. Scales of Notation, Examples VII.b, No. 35