MensaNumber wrote:
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
Hi
MensaNumber,
lets look at the two queries one by one, although they are interlinked..
i)
The GCF of A and B can't be larger than the difference between A and B..As the word GCF suggests, the numbers involved have the GCF as the greatest common factor,
it means both A and B are multiples of the GCF...
therefore
the smallest difference between A and B will be if they are consecutive multiple of GCF.. that is say GCF*2 and GCF *3..
and in this case the difference will be GCF*3-GCF*2=GCF, which means GCF can at max be equal to the difference itself......
only case GCF to be more than difference will be if A=B...
ii)
Consecutive multiples of x have a GCF of x.what are the consecutive multiples of x..
x*1, x*2, x*3, x*4, x*5, x*6...
now as seen x is the only common factor in all the numbers.
1,2,3,4,5,6 do not have any common factor except 1..
this is the reason why consecutive multiples of x have GCF as x..
Hope it helps
_________________