GCF can't be larger than the differebce

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mensanumber: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Wed Oct 23, 2013 6:43 amFollowed by: 1 member; Thanked: 2 times; GMAT Score:750

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?

Thanks

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Source: Beat The GMAT — Problem Solving | Thu Dec 03, 2015 11:35 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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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