Assuming we are talking about positive numbers, remember that any number always has itself and 1 as factors.
Now if the number is prime, then that's all there are, so clearly these aren't prime numbers, because 2 factors is not an odd number of factors.
But any non-prime number has other factor(s), so that means there is a pair of factors that multiply to make the number. A pair is even as well, so maybe you would think that there are no such numbers.
But think about the number 1 itself. Its factors are 1 and itself (but itself is 1) so actually if the pair of factors are the same number, then really there is just one factor! So 1 is one of the numbers that has an odd number of factors.
Can you see now in what case a number has an odd number of factors?
Stephen La Rocque.>