​How many pairs of natural numbers (x, y) exist such that x > y and the product of x, y and HCF (x, y) = 2520?​

Correct option is B

Given:

x > y
x × y × HCF(x,y) = 2520

Formula Used:

HCF(a,b) × LCM(a,b) = a × b

Solution:

Let two numbers → x = Ha and y = Hb

HCF of Ha and Hb = H

Now,

Ha × Hb × H = 2520

​$$H^3 \times a \times b = 2^3 \times 3^2 \times 5 \times 7$$​​

​$$H^3 = 2^3$$

​​$$a \times b = 3^2 \times 5 \times 7$$

Co-prime pair: (9, 35), (45, 7), (63, 5), and (1, 315)

So, 4 pairs of natural numbers.

Thus, the correct answer is (4).