Problem:

3 positive integers are written on a board:

x y z

Person A calculated that the HCF of 2 of the integers and got 1 000 004

Person B did the same and got 1 000 006

Person C did the same and got 1 000 008.

Person D is sure that at least person A, B or C made a mistake, despite the fact they calculated the HCF of different numbers.

Is she right?

Please explain the answer.

Thx.