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What is the greatest common factor of x and y ?

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Re: What is the greatest common factor of x and y ?  [#permalink]

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New post 18 Jun 2018, 20:06
longhaul123 wrote:
0 is also a multiple of every number and in this case if we consider x to be 0 then the GCD is going to 1 ? why shouldnt we consider x to be 0 here ??


Hello

In general when we talk about multiples/factors, we talk about non-zero positive integers only. This is how multiples/factors are defined in my opinion.
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Re: What is the greatest common factor of x and y ?  [#permalink]

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New post 27 Jun 2018, 22:36
did you mean to say that since 0 is a multiple of every integer then 0 can have any factors including 4 . Since the question is stressing on the point that it is just a multiple of 4 so 0 cant be considered.
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What is the greatest common factor of x and y ?  [#permalink]

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New post 12 Dec 2018, 00:52
[quote="stonecold"]A lot of solutions on this page already.
Here is mine
Clearly both 1 and 2 are alone insufficient.
combining them => x=4a y=4b and a=b+1 where b and b+1 will always be coprimes.


stonecold
how do you get a=b+1

If I understand it correctly,

Your solution is as follows:

S1) x=4a, y=4b
S2) x-y=4

S1) & S2) 4(x-y)=4 –> x-y=1 –> 4a-4b=1 –> a=b+1

Since a>b –> gcd(x,y)=gcd(4*(b+1), 4b)=gcd(4b+4-4b,4b)=gcd(4,4b)=4
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What is the greatest common factor of x and y ? &nbs [#permalink] 12 Dec 2018, 00:52

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