Question

the product of two numbers and their HCF is 600 . How many pairs of such numbers (x,y) are there such that x>y​

Answer 1

Answer:

Product of these two numbers = 2160.

HCF of these two numbers = 12.

Therefore, LCM of these two numbers = (2160 / 12) = 180.

So, none of these two numbers is smaller than 12 and larger than 180.

Moreover, both these numbers will be divisible by 12; and 180 should be divisible by both of them.

Step-by-step explanation:

Now, 180 / 12 = 15 = (3*5) = (1*15)

Therefore, the eligible pairs are:

(12*1) & (180 / 1) = 12 & 180

(12*3) & (180 / 3) = 36 & 60

(12*5) & (180 / 5) = 60 & 36

(12*15) & (180 / 15) = 180 & 12

Finally, after avoiding doubling up of pairs, we get two pairs of numbers:

12 & 180

36 & 60.