Classify the following numbers as having odd or even number of factors: (i) 36 (ii) 48 (iii) 65 (iv) 81

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Solution

A number has an odd number of factors when it is a perfect square.
In all other cases, it has an even number of factors. Based on this, we can say that (i) 36 and (iv) 81 have an odd number of factors since 36 = $6^{2}$ and $81 = 9^{2}$ .
(ii) 48 and (iii) 65 cannot be written as squares of a number, so they have an even number of factors.

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