# $2$s in Divisor Product of $36000$

Let $P_n$ be the product of all positive divisors of a positive integer $n$. For example, $P_1 = 1$ and $P_4 = 1 \times 2 \times 4 = 8.$

If $2^m$ is the highest integer power of $2$ that divides $P_{36000}$, what is $m$?

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