Melody....I just read about the proof of this....roughly, it goes
Let n = p^a where p is a prime factor
Then...the divisors of n = p^a are
1, p, p^2, p^3, p^4.......p^a
So...the number of divisors = (a + 1)
So
p^a * q^b where p, q are prime factors
has
(a + 1) (b + 1) divisors
