Question: two numbers have their HCF as 8 and LCM as 1960 .Find the number of such possible pairs.
The factors of 1960 are: 2^3, 5, 7^2 -- note that 2,5,7 are all prime.
Since HCF is 8, then write down the factors as: 8, 5, 7^2
The possible combination of two numbers using these factors, with HCF = 8, is,
(8*1), (8*5*7^2), i.e. (8), (1960)
(8*5), (8*7^2), i.e. (40), (392)
(8*7), (8*5*7), i.e. (56), (280)
There are 3 such pairs: (8, 1969), (40, 392), (56, 280)