{"status": "success", "data": {"description_md": "Mary chose an even $4$-digit number $n$. She wrote down all the divisors of $n$ in increasing order from left to right: $1,2,\\ldots,\\dfrac{n}{2},n$. At some moment Mary wrote $323$ as a divisor of $n$. What is the smallest possible value of the next divisor written to the right of $323$?\n\n$\\textbf{(A) }324 \\qquad\n\\textbf{(B) }330 \\qquad\n\\textbf{(C) }340 \\qquad\n\\textbf{(D) }361 \\qquad\n\\textbf{(E) }646 \\qquad$", "description_html": "<p>Mary chose an even  <span class=\"katex--inline\">4</span> -digit number  <span class=\"katex--inline\">n</span> . She wrote down all the divisors of  <span class=\"katex--inline\">n</span>  in increasing order from left to right:  <span class=\"katex--inline\">1,2,\\ldots,\\dfrac{n}{2},n</span> . At some moment Mary wrote  <span class=\"katex--inline\">323</span>  as a divisor of  <span class=\"katex--inline\">n</span> . What is the smallest possible value of the next divisor written to the right of  <span class=\"katex--inline\">323</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }324 \\qquad\n\\textbf{(B) }330 \\qquad\n\\textbf{(C) }340 \\qquad\n\\textbf{(D) }361 \\qquad\n\\textbf{(E) }646 \\qquad</span> </p>\n<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": 4, "problem_name": "2018 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10B_p22", "prev": "/problem/18_amc10B_p20"}}