Highest Common Factor help

xxravenxx · #1 $Old$ October 18th, 2009, 11:26 PM

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?

Thanks heaps in advance.

tonio · #2 $Old$ October 19th, 2009, 09:17 AM

Quote:

Originally Posted by xxravenxx $View Post$

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?

Thanks heaps in advance.

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

xxravenxx · #3 $Old$ October 27th, 2009, 02:37 AM

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