Question

The number of possible pairs of numbers, whose product is 5400 and HCF is 30, is

Ans given:- 2 pairs

Answer 1

H.C.F of numbers is 30

So required numbers should be multiple of 30.

Let the numbers are 30a and 30b

The product of the numbers = 5400
Then,

30a x 30b = 5400

=> ab = 6

The co-primes or possible pairs of product 6 either (1, 6) and (2,3), or (6,1) and (3, 2)
that means


a x b = 6

30a x 30b = 5400

30 x 180 = (30,180) = 5400 (there (1, 6) a = 1 , b = 6)

60 x 90 = (60,90) = 5400 (there (2, 3) a = 2 , b = 3)

Thus,only two pairs are possible, whose product is 5400 and H.C.F. is 30.