Binomial Expansion and Factorials

Probability Level 2

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

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