Perfect squares have an odd number of factors.
If f is a factor of N, then so is N/f. (For example, 3 is a factor of 30, and so is 10). Thus, it seems factors come in pairs, and there should always be an even number of them. But if f = N/f, then these two factors are the same, resulting in an odd number of factors. For example, 3 is a factor of 9, and it's "mate" is also 3.
So for the numbers with an odd number of factors, there is some f where f=N/f. Multiplying both sides by f, we have f^2 = N. So this happens when N is a perfect square.
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Yes. Square numbers have an odd number of factors. 49 has three factors.
Square numbers have an odd number of factors.
All odd numbers have odd factors.
Odd.
Because 55 is an odd number. All the factors of odd numbers are odd.