eight divisors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. However, the number of positive divisors is not a totally multiplicative function: if the two numbers and share a common divisor, then it might not be true that The sum of the positive divisors of is another multiplicative function (for example, ). Both of these functions are examples of divisor functions.

If the prime factorization of is given by
: then the number of positive divisors