mock que - how to solve this

let x = d·a and y = d·b where gcd(a, b) = 1

then

x·y·gcd(x,y) = (d·a)(d·b)(d) = d³ab = 1080

so we need d³ab = 1080

prime factorize:

1080 = 2³ · 3³ · 5

now distribute powers between d³ and ab

since d³ has powers in multiples of 3, possible d:

d = 1, 2, 3, 6

now for each d, compute ab = 1080 / d³

d = 1 → ab = 1080 = 2³·3³·5 → primes = 3 → unordered coprime splits = 2^(3−1) = 4

d = 2 → ab = 1080 / 8 = 135 = 3³·5 → primes = 2 → ways = 2^(2−1) = 2

d = 3 → ab = 1080 / 27 = 40 = 2³·5 → primes = 2 → ways = 2

d = 6 → ab = 1080 / 216 = 5 → primes = 1 → ways = 1

total = 4 + 2 + 2 + 1 = 9

answer = 9

you got 4 because you probably only counted the d = 1 case and missed the other possible gcd values

Aapko pura solution samajh nahi aaya ya some part of it?

Let me know and I will try to explain it in a more simple way.