2022 Fermat Problem 16

The remainder when 111 is divided by 10 is 1. The remainder when 111 is divided by the positive integer n is 6. The number of possible values of n is

\textbf{(A)}\ 5\quad \textbf{(B)}\ 8\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 4

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.