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Remainder and gcf concept

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Remainder and gcf concept [#permalink]

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New post 29 Jun 2009, 22:32
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I found this on another forum

Question is -

The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r >1?

1) the greatest common factor of m and p is 2.
2) the least common multiple of m and p is 30.


One of the explanations says

Quote:
when a number X is divided by number Y then the remainder left is always a multiple of HCF of X and Y ( provided x and y are integers) hence A is sufficient


Can someone please explain this? Why is this always true?

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Re: Remainder and gcf concept [#permalink]

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New post 30 Jun 2009, 00:25
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n = x*GCF(m,n)
m = y*GCF(m,n)

since m>n; y>x

m = t*n + r

since m>n; t>=1

r must be greater than 0 else GCF(m,n) would be n. And it is given that n is not a factor of m.

m = t*x*GCF(m,n) + r
y*GCF(m,n)=t*x*GCF(m,n) + r
(y-t*x)*GCF(m,n)=r

y-t*x>0 because r>0
Than r is divisible by GCF(m,n)

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Re: Remainder and gcf concept [#permalink]

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New post 30 Jun 2009, 09:47
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thanks! very good explanation.

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Re: Remainder and gcf concept [#permalink]

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New post 30 Jun 2009, 23:12
Thanks to you. You gave me an opportunity to think about a question that I've never tought about before.

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Re: Remainder and gcf concept [#permalink]

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New post 03 Jul 2009, 23:32
Guys please ignore if i ask a real dumb question.........but

Whenever we divide a bigger number with a smaller don't you agree that the remainder will be always > 1???

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Re: Remainder and gcf concept [#permalink]

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New post 04 Jul 2009, 04:00
730 divided by 9; remainder is 1 ;)

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Re: Remainder and gcf concept [#permalink]

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New post 04 Jul 2009, 06:39
mdfrahim wrote:
Guys please ignore if i ask a real dumb question.........but

Whenever we divide a bigger number with a smaller don't you agree that the remainder will be always > 1???


* When you divide 4 by 3, the remainder is 1.
* When you divide 6 by 3, the remainder is 0.

When you divide an integer x by a positive integer d, all you can be sure of, without more information, is that the remainder is an integer between 0 and d-1, inclusive.
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Re: Remainder and gcf concept [#permalink]

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New post 04 Jul 2009, 11:44
hx. maliyeci and Ianstewart. I got the point now.

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Re: Remainder and gcf concept [#permalink]

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New post 04 Jul 2009, 22:55
A.

There is pattern to remainders. Please verify as this is my own finding , no source to quote :-)

1. EVEN/EVEN = EVEN REMAINDER
2. EVEN/ODD = ODD REMAINDER
3. ODD/ODD = CAN BE ANYTHING
4. ODD/EVEN = ODD REMAINDER


Stmt 1 -
This tells us that both the numbers are even hence there remainder had to be even so it had to be >1 .

Stmt 2 -
Plug the numbers.

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Re: Remainder and gcf concept   [#permalink] 04 Jul 2009, 22:55
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