$N = 2^{3} \times 5^{3}$ . How many sets of two distinct factors of N are co-prime to each other?

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Solution

The correct option is B 24
For $N = 2^{3} \times 5^{3}$
The number of sets of factors co-prime to each other = (x + 1)(y + 1) + xy = (3 + 1)(3 + 1) + 3 $\times$ 3 = 25. However, for co-prime set (1,1), factors are not distinct. Therefore, number of sets = 25 - 1 = 24.

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