what relationships can you find between the number of positive factors of a number, and the prime factorization of a number?

Question

what relationships can you find between the number of positive factors of a number, and the prime factorization of a number? For instance, the prime factorization of 4 is 2^2, while 4 had 3 positive factors: 1,2, and 4. The prime factorization of 6 is 2x3, while 6 has 4 positive factors: 1,2,3, and 6.

Answer 1

Since 1 is not prime, there will be at least one extra factor.

Since the number is, in and of itself, a factor, then it too will be a factor, causing at most

two extra positive factors than prime factors