Question

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

• A. 12
• B. 24
• C. 23
• D. 11

Answer 1

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.