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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

That quote quote is not correct. According to Wikipedia the GCD or HCF can be extended to rationals ( fractions ).

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

So.....How is it done ???

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

There are algorithms to compute the GCD (HCF). But for these problems they are not necessary.

Look at the example you gave.

1/2 and 1/6

If you take the smaller of the two and divide both 1 / 2 and 1 / 6 by it what do you get?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

gives me 3 gives me 1

but I'm not sure of understanding what I'm doing

*Last edited by Al-Allo (2013-07-04 02:35:00)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

Hi;

You need help with that division?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

bobbym wrote:

Hi;

You need help with that division?

Why, my answer isn't correct ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

You answer is correct, but then you said you did not understand what you were doing. Which part?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Well, I don't understand how we find a factor of two fractions, that's what xD So, I wasn't sure how dividing my two fractions by 1/6 would give me my answer to my initial question... Thank you for your help

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

If you have two numbers or fractions what is the biggest number that can go into the smaller number?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

the biggest comon divisor

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

Say you have 18 and 6. The smaller number is 6. if you divide both numbers by the smaller number you get 1 and 3. How do you now know that you have found the GCD?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

because you took the smallest number between the two and it went even in the biggest number

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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But how do you know there isn't a larger factor?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

bobbym wrote:

But how do you know there isn't a larger factor?

Not sure what other explanation I can give

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Anyway, the reason why I asked you how to find a common factor of two fractions was because of this...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

The reason you know you found the gcd is becuase the GCD is the biggest number that goes into both. When you use the smaller one you know you have the biggest one obviously for the smaller. If it goes into the larger you know there can be nothing bigger because it will not go into the smaller number.

And -2cd is a common factor of those two monomials.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

But you said earlier that neither -2cd or 2cd was good.....

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

As the GCD we do not know yet but as a factor it is okay.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

bobbym wrote:

As the GCD we do not know yet but as a factor it is okay.

Ah ok. Still, as I see, I'm lacking knowledge of basic things xD Oh well, Atleast I can continue to learn about it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,229

Hi;

I have to go offline until later see you then.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Bye Bye ! Thank you again!

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**{7/3}****Member**- Registered: 2013-02-11
- Posts: 210

my old textbook says gcd(a/b,c/d) = gcd(a,c)/lcm(b,d)

*Last edited by {7/3} (2013-07-04 20:48:20)*

There are 10 kinds of people in the world,people who understand binary and people who don't.

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