2009 AMC 12A 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\qquad \textbf{(B)}\ 7\qquad \textbf{(C)}\ 8\qquad \textbf{(D)}\ 9\qquad \textbf{(E)}\ 10

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