Question

How many pairs of natural numbers exist whose product is 180 and HCF is 5.

Answer 1

Let the number be 5a and 5b, where a and be are two number prime to each other. 

∴ 5a x 5b = 180
∴ ab = 7.2
Now, the pairs of number whose products is 7.2, are (7.2, 1)

So, the required numbers are (5 x 1, 5 x 7.2).