AMC 12 2009a Problem 18

For $k > 0$, let $I_k = 10\ldots 064$, where there are $k$ zeros between the $1$ and the $6$. Let $N(k)$ be the number of factors of $2$ in the prime factorization of $I_k$. What is the maximum value of $N(k)$?

\textbf{(A)}\ 6 \textbf{(B)}\ 7 \textbf{(C)}\ 8 \textbf{(D)}\ 9 \textbf{(E)}\ 10