2021 AMC 12B Problems/Problem 15

Revision as of 17:34, 11 February 2021 by Sugar rush (talk | contribs)

Problem 15

The number $2021$ is expressed in the form \[2021=\frac{a_1!a_2!...a_m!}{b_1!b_2!...b_n!},\] where $a_1 \geq a_2 \geq \cdots \geq a_m$ and $b_1 \geq b_2 \geq \cdots \geq b_n$ are positive integers and $a_1+b_1$ is as small as possible. What is $|a_1 - b_1|$?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$