Question

hcf of two numbers is 12 and their difference is also 12.which of the following can be the numbers​

Answer 1

Answer:

84,96

Solution:

let the numbers be 12a, 12b where gcd(a,b)=1. (by the definition of H.C.F

Also,12b-12a=12 b-a=1

So,we are left with two equations,

gcd(a,b)=1

b-a=1

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

(a,b)=(1,2)(2,3)(3,4)(4,5)

Which means,

(12a,12b)

=(12,24)(24,36)(36,48)(48,60),(60,72),(72,84),(84,96),.........