{"status": "success", "data": {"description_md": "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 $N(k)$?\n\n$\\textbf{(A)}\\ 6\\qquad \\textbf{(B)}\\ 7\\qquad \\textbf{(C)}\\ 8\\qquad \\textbf{(D)}\\ 9\\qquad \\textbf{(E)}\\ 10$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For  <span class=\"katex--inline\">k &gt; 0</span> , let  <span class=\"katex--inline\">I_k = 10\\ldots 064</span> , where there are  <span class=\"katex--inline\">k</span>  zeros between the  <span class=\"katex--inline\">1</span>  and the  <span class=\"katex--inline\">6</span> .  Let  <span class=\"katex--inline\">N(k)</span>  be the number of factors of  <span class=\"katex--inline\">2</span>  in the prime factorization of  <span class=\"katex--inline\">I_k</span> .  What is the maximum value of  <span class=\"katex--inline\">N(k)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 6\\qquad \\textbf{(B)}\\ 7\\qquad \\textbf{(C)}\\ 8\\qquad \\textbf{(D)}\\ 9\\qquad \\textbf{(E)}\\ 10</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p19", "prev": "/problem/09_amc12A_p17"}}