How do you find the number of positive factors a particular integer has?
For example, how many postitive factors does 96 have?
To find the number of factors of N
1) Find the prime factorization of N
N = (2a)(3b)(5c)…
2) Collect the set of exponents of the prime factors:
{a, b, c, …}
3) Add one to every member of this set:
{a + 1, b + 1, c + 1, …}
4) Find the product of every number in this latter set. That product is the number of factors of N. This count includes 1 (the factor of every number) and N.
For example, 96 = (32)(3) = (25)(31)
The set of exponents is {5, 1}. Add one to each, and we have {6, 2}. The product, 6(2) = 12, is the number of factors of 96. These 12 factors include both 1 and 96.