Binomial Expansion and Factorials

Probability Level 2

A=1×2××100B=1×2××200 \begin{aligned} A &=& 1\times2\times\cdots \times 100 \\ B &=& 1\times2\times\cdots \times 200 \end{aligned}

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

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