Question

the h.c.f. of two numbers is 12 and their difference is 12 . the numbers are?

Answer 1

Dear friend,

Let numbers be 12x and 12y where x and y are both co-prime numbers

$|12x - 12y| = 12$

$12 |x - y| = 12$

$|x - y| = \frac{12}{12} = 1$

So there can be many possibilities,

x = 2 , y = 1
So they can be 24 and 12.

x = 3 , y = 2
So they can be 36 and 24.

x = 5 , y = 4
So they can be 60 and 48.

Hope it helps !!!

Answer 2

Let the two numbers be 12a and 12b where a and b are co-prime and (a > b )

$=> 12a - 12b = 12$

$=> a - b = 1$

Put any value for a and b satisfying above condition and you get different pairs.

For example (a ,b) = (3,2) give 36 & 24

(4,3) gives 48 & 36

(5,4) gives 60 & 48 and so on.

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