Binomial Expansion and Factorials

\[ \begin{eqnarray} A &=& 1\times2\times\cdots \times 100 \\ B &=& 1\times2\times\cdots \times 200 \end{eqnarray} \]

It's obvious that \(B\div A \) is an integer.
Is it also true that \(B\div A \div A\) is still an integer?

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