Rationals from 25!

Find the number of rational numbers \(0 \leq \dfrac{p}{q} \leq 1\) are there such that \(\gcd(p,q) = 1\) and \(pq = 25!\).

Notation: \(!\) denotes the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).


Inspired by Aman Rajput.

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