# Thread: Highest Common Factor help

1. ## Highest Common Factor help

Help with this problem please too hard:

Three positive integers are written on a whiteboard. David calculated the highest common factor of the two of them and obtained 1 000 004. Rose and Stephen did the same obtaining the results 1 000 006 and 1 000 008 respectively. Emily is sure at least one of her friends made a mistake despite the fact that they calculated the highest common factors of different numbers. Is she right?

2. Originally Posted by xxravenxx
Help with this problem please too hard:

Three positive integers are written on a whiteboard. David calculated the highest common factor of the two of them and obtained 1 000 004. Rose and Stephen did the same obtaining the results 1 000 006 and 1 000 008 respectively. Emily is sure at least one of her friends made a mistake despite the fact that they calculated the highest common factors of different numbers. Is she right?

Well, the maximal power of two that divide the numbers are:

== 1,000,004 is divisible by 2^2

== 1,000,006 is divisible by 2

== 1,000,008 is divisible by 8

Let A,B,C the numbers, and assume LCM(A,B) = 1,000,004 ==> none of A,B is divisible by 2^3 or higher powers of 2 ==> check this doesn't make sense with the other two: LCM(A,C) and LCM(B,C), no matter how we order them.

Tonio

3. Can you elaborate please? I don't understand you.