Question

Hcf if two numbers is 90 and their product is 97200 how many such pairs exist

Answer 1

Hi there!
Here's the answer :

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Given,
For two Numbers,

HCF = 90
Product = 97200

Let the numbers be 90a & 90b
Then, 90a × 90b = 97200
=> ab =97200/(90×90)
=> ab = 12

Now, coprimes with product 12 are :
(1, 12) & (3,4)

So the Required No.s are:
(90×1 , 90×12) & (90×3 , 90×4)

Clearly , there are 2 Such pairs.

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:)

Hope it helps

Answer 2

Two numbers will be having 90 as hcf so let those two numbers be 90x and 90y

90x X 90y = 97200

xy=97200%3600=12

12=3 x 4 or we say 12= 2 x 2 x 3

so one pair can me (2x90) x (6x90) =180 x 540.

and other pair can be (4x90) x (3x90)= 360 x 270.