Numbers that have an odd number of factors are?

Answer 1

Perfect squares ( also called square numbers) have an odd number of factors and primes squared have 3 factors.

Brief Explanation:

If you start with a Prime number, it has 2 factors by definition. Square that number and you have 3 factors, which is an odd number. So primes squared always have an odd number of factors. For example, 5 has 1 and 5 as factors, 25 has 1,5, and 25.

What about an odd number such as 21 which is not the square of a prime. It has factors 1, 21, 3 and 7 so an even number of factors. How about 27, 1,27, 3, 9 once again even.

What I was trying to show is that factors of numbers come in pairs and so only certain numbers will have an odd number of factors. Let's look at one more perfect square that is not a prime squared. How about 16 which is 4 squared.

The factors are 1,2,4,8,and 16 which is an odd number of factors.

Looking at these as pairs we see the factor pairs of 16 are 1 x 16, 2 x 8, and 4 x 4, giving us the factors of 1, 2, 4, 8, and 16 - an odd number of factors.

So we conclude that perfect squares have an odd number of factors and primes squared have 3 factors.

Answer 2

They are square numbers.