Question

If n=(2^3)*(3^2) ,then how many sets of 2 distinct factors of n are coprime to each other

Answer 1

1 set of 2 distinct factors

Answer 2

Answer:

17 pairs

Step-by-step explanation:

We can simply use formula to calculate sets of factors which are coprime to each other,

n=(2^3)*(3^2)….assume p=3, q=2 If N = a^p × b^q,

[(p + 1) (q + 1) – 1] + p × q

[(3+1) (2+1)-1] + 3*2

((4*3)-1) + 6

11+6

=17

In total, 17 cases are possible –

(1, 2), (1, 3), (1, 4), (1, 6), (1, 8), (1, 9), (1, 12),

(1, 18), (1, 24), (1, 36), (1, 72) (2, 3), (2, 9), (4, 3),

(4, 9), (8, 3) and (8, 9).