Question

The hcf of two numbers is 12. What could these two numbers be?

Answer 1

Answer:

Since the HCF of the two numbers is 12 the

numbers are 12a and 12b where a and b are

prime to each other

Given 12a−12b=12 ⇒ a−b=1

⇒ a and b are consecutive numbers that are prime

to each other. By inspection we can see that

84, 96 i.e. 12 x 7 and 12 x 8 are the two

numbers satisfying this condition (8−7=1)