N=2^4*3^8*5^2*7^2==128,595,600
128595600 = 2^4 * 3^8 * 5^2 * 7^2. As you can see, it has 4 DISTINCT prime factors{2, 3, 5, 7}
Counting the repeats, then just add the exponents up:4 + 8 + 2 + 2 ==16 prime factors.
If you want to know the number of "DIVISORS", then it has:
[4+1] * [8+1] * [2+1] * [2+1] ==5 x 9 x 3 x 3 ==405 DIVISORS.
