1951 AHSME 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}\qquad\textbf{(B)}\ 11\text{ only}\qquad\textbf{(C)}\ 13\text{ only}\qquad\textbf{(D)}\ 101\qquad\textbf{(E)}\ 1001

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.