{"status": "success", "data": {"description_md": "For some positive integer $n,$ the number $110n^3$ has $110$ positive integer divisors, including $1$ and the number $110n^3.$ How many positive integer divisors does the number $81n^4$ have? \n\n$\\textbf{(A)}\\ 110\\qquad\\textbf{(B)}\\ 191\\qquad\\textbf{(C)}\\ 261\\qquad\\textbf{(D)}\\ 325\\qquad\\textbf{(E)}\\ 425$\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 some positive integer  <span class=\"katex--inline\">n,</span>  the number  <span class=\"katex--inline\">110n^3</span>  has  <span class=\"katex--inline\">110</span>  positive integer divisors, including  <span class=\"katex--inline\">1</span>  and the number  <span class=\"katex--inline\">110n^3.</span>  How many positive integer divisors does the number  <span class=\"katex--inline\">81n^4</span>  have?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 110\\qquad\\textbf{(B)}\\ 191\\qquad\\textbf{(C)}\\ 261\\qquad\\textbf{(D)}\\ 325\\qquad\\textbf{(E)}\\ 425</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": "2016 AMC 12A Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p19", "prev": "/problem/16_amc12A_p17"}}