you mean there will exist a 1-1 correspondence between power set of a set A with cardinality n and the set of positive factors of the product of n primesIn any factor you come up with, it will either be divisible by one of the n unique primes, or not. Whether or not your particular factor is divisible by a prime is independent of whether your factor is divisible by another prime; so how many ways can you make a factor if you have to make n yes/no decisions?
Think about it as a prime factor set. You're finding the cardinality of the power set...
what about if the primes are not distinct? i don't the number of positive factor will be 2^n, it will be less than that.Yes. Hence the 2^n.