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22 Jun 2010, 19:33
Kudos
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can someone explain the following statement? thanks!
the greatest common factor of M and N can't be larger than the difference between M and N.
why is it so?
the greatest common factor of M and N can't be larger than the difference between M and N.
why is it so?
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22 Jun 2010, 21:46
Kudos
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The greatest common factor is the largest number that divides evenly into both numbers.
The difference between M and N actually represents the maximum interval between them that also represents the maximum possible factor tht would evenly divide both M and N.
For eg. For 36 and 48, the difference is 12, and we also note that the GCF is 12. The GCF cannot be any number greater than 12. Eg. if you tried 18, though it evenly divides 36, 48 is only 12 greater than 36 and would therefore lie before the next multiple of 18 which is 54.
In other words the difference between 2 numbers also represents the greatest possible interval between the two numbers and hence also the greatest possible factor of those two numbers.
Hope this makes sense, Good luck!
The difference between M and N actually represents the maximum interval between them that also represents the maximum possible factor tht would evenly divide both M and N.
For eg. For 36 and 48, the difference is 12, and we also note that the GCF is 12. The GCF cannot be any number greater than 12. Eg. if you tried 18, though it evenly divides 36, 48 is only 12 greater than 36 and would therefore lie before the next multiple of 18 which is 54.
In other words the difference between 2 numbers also represents the greatest possible interval between the two numbers and hence also the greatest possible factor of those two numbers.
Hope this makes sense, Good luck!
