{"status": "success", "data": {"description_md": "A positive integer $n$ has $60$ divisors and $7n$ has $80$ divisors.  What is the greatest integer $k$ such that $7^k$ divides $n$?\n\n$\\mathrm{(A)}\\ {{{0}}} \\qquad \\mathrm{(B)}\\ {{{1}}} \\qquad \\mathrm{(C)}\\ {{{2}}} \\qquad \\mathrm{(D)}\\ {{{3}}} \\qquad \\mathrm{(E)}\\ {{{4}}}$\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>A positive integer  <span class=\"katex--inline\">n</span>  has  <span class=\"katex--inline\">60</span>  divisors and  <span class=\"katex--inline\">7n</span>  has  <span class=\"katex--inline\">80</span>  divisors.  What is the greatest integer  <span class=\"katex--inline\">k</span>  such that  <span class=\"katex--inline\">7^k</span>  divides  <span class=\"katex--inline\">n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ {{{0}}} \\qquad \\mathrm{(B)}\\ {{{1}}} \\qquad \\mathrm{(C)}\\ {{{2}}} \\qquad \\mathrm{(D)}\\ {{{3}}} \\qquad \\mathrm{(E)}\\ {{{4}}}</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": 5, "problem_name": "2005 AMC 12B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc12B_p22", "prev": "/problem/05_amc12B_p20"}}