AHSME 1951 Problem 19

A six place number is formed by repeating a three place number; for example, $256256$ or $678678$, etc. Any number of this form is always exactly divisible by: $\textbf{(A)}\ 7 \text{ only} \textbf{(B)}\ 11 \text{ only} \textbf{(C)}\ 13 \text{ only} \textbf{(D)}\ 101 \textbf{(E)}\ 1001$