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=62 and 81=92.
(ii) 48 and (iii) 65 cannot be written as squares of a number, so they have an even number of factors.