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# What is the greatest common factor of positive integers x

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Manager
Joined: 12 Feb 2006
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What is the greatest common factor of positive integers x [#permalink]  10 Feb 2007, 22:17
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What is the greatest common factor of positive integers x and y?

1. The greatest common factor of x/2 and y/2 is 5.

2. X and Y are even.

Thanks,
Director
Joined: 12 Jun 2006
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E?

Don't X and Y say the same thing, they are even #s.
Director
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I choose A.

if x/2 and y/2 have a gcf of 5 it means that x and y have only two factors (= 5 and 2)... in common. Thus gcf of x and y=10

Some examples:

(2*5*5*5)/2 and (2*5)/2 : gcf=5; x and y gcf=10
(2*2*5*5)/2 and (2*5)/2 : gcf=5; x and y gcf=10
(2*3*3*5)/2 and (2*5)/2 : gcf=5; x and y gcf=10
(2*5*5*7)/2 and (2*3*5)/2 : gcf=5; x and y gcf=10
Senior Manager
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I'm not good with LCM and GCM. However, I will try to solve this one.

What is the GCM(x,y)?

(1) GCM(x/2, y/2) = 5
Assuming m not= n. Both m and n do not share any common factor.
x/2 = m x 5
y/2 = n x5

If we set the equation above, we can be certain that the GCM(x/2, y/2) = 5

x = 2 x 5 x m
y = 2 x 5 x n

Since m not= n
GCM(x,y) = 2 x 5 = 10 SUFF

(2) will come back to this one later :p

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