What Are Proper Factors?

Proper factors are factors of a number N that are neither N nor 1. In general, a factor of N is a whole number, or integer, that divides N without a remainder.

For example, the factors of 20 are 1, 2, 4, 5, 10 and 20. The proper factors of 20 are 2, 4, 5 and 10. Usually, when factoring a number, it is desirable to report only the prime factors, or factors that are also prime numbers. The prime factorization of 20 excludes 4 and 10, because both of these numbers are divisible by 2, and 10 is also divisible by 5.