Why does a square number always have an odd number of factors?

Answer 1

Factors can be listed as factor pairs. With square numbers, one of those pairs will be the same number twice. When written as a list, only one of them will be used, leaving an odd number of factors.

Answer 2

One of the factor pairs for a square number will be the same number twice. When you list the factors, you only need to write that number once. That will leave you with an odd number of factors.