Number of Proper factors

75600=17^2.2^4.5^2
so number of factors=(2+1)(4+1)(2+1)=40

justification
if N=a^p.b^q.c^r...
so all factors of N are terms of the expansion of
(!+a+a^2+...+a^p)(1+b+b^2+...+b^q)(1+c+c^2+...+c^r)...
so number of factors = number of terms of the above expansion
which is precisely (p+1)(q+1)(r+1)...

i don think 17².2⁴.5² =75600 rather its115600

Thank you
:-)