I've been trying to find / generate a formula for the following problem:
- Given a number, how many positive integers are factors of this number.
In practice, you could simply build a table as such (lets assume the number is 36):
1 | 36
2 | 18
3 | 12
4 | 9
6 | 6
Thus there are 9 positive integers that are factors to 36.
This method seems like it would be taxing if the number was large. So I was thinking that if you knew the prime factorization for a number such as $\,2 \cdot 2 \cdot 3 \cdot 3 = 36, \,$ there should be a formula for the number of unique combinations you can multiply these prime factors together. That's where I am stuck. Thanks in advance!