$2$ s in Divisor Product of $36000$

Number Theory Level 3

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 $m$ ?

222s in Divisor Product of 360003600036000