Do all square numbers have an odd number of factors?

Yes, they do.

Factors come in pairs. When a number is squared it is only one factor.

Example:

16

2x8 = 2 factors

4x4 = 1 factor

1x16 = 2 factors

Total = 5 factors

***

That's true of integers (whole numbers) that are perfect squares.

It turns out that every whole number has an even number of factors, but if the

number is a perfect square, then two of them are the same number, so there

appear to be an odd number of them.