Greatest common factor

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katherinejane: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Nov 21, 2012 3:56 pm

by katherinejane » Thu Dec 20, 2012 6:26 pm

Apologies if this has already been asked- but why is it that the GCF of x and y can't be > m - n?

Also, why is the GCF of consecutive multiples of 'n', n?

Many thanks in advance

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 20, 2012 6:26 pm

puneetkhurana2000: Master | Next Rank: 500 Posts; Posts: 131; Joined: Wed Nov 14, 2012 2:01 pmFollowed by: 2 members; Thanked: 39 times

by puneetkhurana2000 » Thu Dec 20, 2012 6:34 pm

I did not understand your first question as it is not clear what is x,y, m or n? Please rephrase it clearly.

For second question let us say n = 2, so consecutive multiples of 2 are 2,4,6,8,10.....

The Greatest Common factor of 2(2*1),4(2*2),6(2*3),8(2*24),10(2*5)..... is 2, which is equal to n.

Hope this makes sense!!!

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puneetkhurana2000: Master | Next Rank: 500 Posts; Posts: 131; Joined: Wed Nov 14, 2012 2:01 pmFollowed by: 2 members; Thanked: 39 times

by puneetkhurana2000 » Thu Dec 20, 2012 7:29 pm

I believe your first question is:- why the GCF of x and y can't be > x - y?

This is only possible if x and y are distinct; x and y are not consecutive multiples of a certain number.

e.g. x = y = 10. GCF = 10 is > 10 - 10 (0)

e.g. x = 2, y = 4. GCF = 2 is = 4 - 2 (2)

For all cases GCF can't be greater than the difference.

e.g. x = 12, y = 28. GCF = 4 is < 28 - 12 (16)

e.g. x = 5, y = 3. GCF = 1 is < 5 - 3 (2)

Note:- Maximum value of GCF of x and y can be smaller of the two values(cases such as x =4, y = 8 and GCF is 4 here) in all other cases GCF will always be 1 <= GCF <= smaller of the two values.

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