I understand in order to find number of divisors, you need to follow following method, But I don't seem to find why it works.
In order to find number of divisors a number has, you find the prime factorization, and add one to exponents and multiply them.
The number 48 has how many positive integral divisors?
a. First find the prime factorization: $2^4$ x $3^1$.
b. Adding 1 to each exponent we get: 4+1 and 1+1 or 5 and 2.
c. Multiplying these numbers together we get 10.
d. The answer is 10.
Can anyone explain or give me resources behind the logic of this method.