2011 AMC 12B Problem 15

How many positive two-digit integers are factors of $2^{24}-1$ ?

$\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 8 \qquad \textbf{(C)}\ 10 \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 14$

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