2021 AMC 12B Problems/Problem 15

The following problem is from both the 2021 AMC 12B #15 and 2021 AMC 10B #20, so both problems redirect to this page.

Problem

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 $|a_1 - b_1|$ ? $\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5$

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2021 AMC 12B Problems/Problem 15

Problem