2009 AMC 10A Problem 25

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)?

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

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