Question

the HCF of two number is 12 and their difference is also 12 the number are​

Answer 1

Answer:

Let the numbers be [math]12a, 12b[/math] where [math]gcd(a, b) = 1[/math]. (By the definition of HCF).

Also, [math] 12b - 12a = 12[/math].

[math] \implies b-a = 1 [/math]

So, we are left with two equations,

[math]gcd(a, b) = 1 [/math] and

[math] b-a = 1 [/math]

Which is true for all adjacent pairs of natural numbers. Therefore,

[math](a, b) = {(1,2) (2, 3), (3, 4), (4,5),…}[/math]

Which means,

[math] (12a, 12b) = {(12, 24), (24, 36), (36, 48), (48, 60), …}[/math]

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Answer 2

Answer:

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