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GCF can't be larger than the differebce

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by mensanumber » Thu Dec 03, 2015 11:35 pm
Hi Math Experts:
I have hard time getting my head around these following two concepts-
1) The GCF of A and B can't be larger than the difference between A and B
2) Consecutive multiples of x have a GCF of x.

I was wondering if you guys could elucidate them?

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by Brent@GMATPrepNow » Fri Dec 04, 2015 7:04 am
mensanumber wrote: I have hard time getting my head around these following two concepts-

1) The GCF of A and B can't be larger than the difference between A and B

2) Consecutive multiples of x have a GCF of x.
Perhaps some examples will help.

1) The GCF of A and B can't be larger than the difference between A and B
Say we have two big numbers like 4348 and 4388
4388 - 4348 = 40
So, we can conclude that the GCF of 4348 and 4388 must be less than or equal to 40


Consecutive multiples of x have a GCF of x
455 and 460 are consecutive multiples of 5, so the GCF of 455 and 460 must be 5.
Likewise, 567 and 574 are consecutive multiples of 7, so the GCF of 567 and 574 must be 7

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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