{"status": "success", "data": {"description_md": "Suppose that $d_1$ is a divisor of $2024^4$ such that if a second divisor $d_2 \\neq d_1$ were chosen at random, there would be a $\\tfrac{1}{3}$ chance that $d_1d_2$ is a factor of $2024^4$ as well. Given that the sum of all possible $d_1$ is $S$, how many factors does $S$ have?  \n  \n$\\textbf{(A)}~18\\qquad\\textbf{(B)}~36\\qquad\\textbf{(C)}~48\\qquad\\textbf{(D)}~96\\qquad\\textbf{(E)}~150$", "description_html": "<p>Suppose that <span class=\"katex--inline\">d_1</span> is a divisor of <span class=\"katex--inline\">2024^4</span> such that if a second divisor <span class=\"katex--inline\">d_2 \\neq d_1</span> were chosen at random, there would be a <span class=\"katex--inline\">\\tfrac{1}{3}</span> chance that <span class=\"katex--inline\">d_1d_2</span> is a factor of <span class=\"katex--inline\">2024^4</span> as well. Given that the sum of all possible <span class=\"katex--inline\">d_1</span> is <span class=\"katex--inline\">S</span>, how many factors does <span class=\"katex--inline\">S</span> have?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~18\\qquad\\textbf{(B)}~36\\qquad\\textbf{(C)}~48\\qquad\\textbf{(D)}~96\\qquad\\textbf{(E)}~150</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2024 Mock AMC 10 - Problem 17", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}