Talk:Greatest common divisor

Example is redundant

Oops, maybe I shouldn't have put in an example of Euclid's algorithm, since such an example is already given on the Euclid's algorithm page. --Catherine Woodgold 08:38, 13 May 2007 (CDT)

Why so complicate?

$60=2^{2}\times 3^{1}\times 5^{1}$

$72=2^{3}\times 3^{2}\times 5^{0}$

So for the gcd you have take take the smallest exponents: :$\operatorname {gcd} (60,72)=2^{2}\times 3^{1}\times 5^{0}=4\times 3=12$

lcm is similar: You have to take the gratest exponents: :$\operatorname {lcm} (60,72)=2^{3}\times 3^{2}\times 5^{1}=8\times 9\times 5=360$

--arbol01 19:01, 15 July 2007 (CDT)

That's what the article says. Are you suggesting that there's some difference between what you wrote above and what the article says? Michael Hardy 09:38, 16 July 2007 (CDT)

highest common factor?

In number theory, I never read the term "highest common factor", but my Oxford dictionary and google seem to know it quite well. Is this perhaps a term used at school level? Peter Schmitt 23:41, 26 June 2009 (UTC)

Subpage "Examples" or "Tutorial"?

The detailed examples should go on a subpage (Example, Tutorial?). Or is this what is meant by "Student level"? Then the name is a bad choice (at least for mathematics). Peter Schmitt 23:07, 27 June 2009 (UTC)

I just saw that there is a "Tutorials" subpage. That seems to fit in this case. In other cases "Example(s)" would be better. Peter Schmitt 23:53, 29 June 2009 (UTC)

Tutorial pages were added to Citizendium between the last revision before yours and your latest revisions. I'm not sure what their specific purpose is. The tutorial page doesn't give any description standardizing their purpose. Perhaps you are right that for a topic such is this, it should provide more extensive examples.

However, I don't really like the new version better than the old. Certainly some things are good additions -- mentioning relatively prime, for instance. But I don't think the existence of a tutorials page should preclude including an example or two on the main page. I like the old example better then the ones you added, both for formatting and content. The new examples are hard to read. They also involve applying a theorem, namely, that to compute a GCD, you can first factor (which requires knowing about the Unique Factorization theorem), then use the largest of the exponents common to each number to form the factorization of the GCD. I think the description of finding the GCD by enumeration as was originally done is conceptually simpler and doesn't require the uninformed reader to consult another page.

Even if there is consensus that the new type of example is preferable, the statement of the theorem that is used in the computation comes after the example itself. This is a particular instance of bad organization in the current revision. There is no introduction, and the topics seem haphazardly thrown together. Are there any thoughts from others on whether to modify the current version, combine it with the old, or to revert to the old completely with a few necessary additions (relatively prime, pairwise relatively prime, alternate definitions (or characterizations?) of GCD...)? Also, does anyone know of a post somewhere discussing the specific intention of a tutorials page?Barry R. Smith 04:06, 22 July 2009 (UTC)

Fixing mistake

Suppose the two numbers being examined are 12 and 24. What's the greatest common divisor? 12. It's not less than 12. It's not between 1 and 12. It IS 12. The wording the greatest common divisor of some numbers is a number between 1 and the smallest of the numbers suggests that the number is between 1 and the smaller of the numbers, namely 12. The gcd IS 12. The revised wording is right.--Thomas Wright Sulcer 02:32, 20 April 2010 (UTC)

Yes, but 1 is also possible. Boris Tsirelson 07:23, 20 April 2010 (UTC)

I would say that between is ambiguous, but not incorrect. As a non-expert in this field, I would say that your current solution "the greatest common divisor of any numbers is a number greater than or equal to 1 and less than or equal to the smallest of the numbers" is one heck of a mouthful. I would suggest that a more readable say of putting this would be "the greatest common divisor of some numbers is a number between 1 and the smallest of the numbers inclusive", which clears up any ambiguity. However, I have no expertise in this field so I shall not make the edit. --Chris Key 10:44, 20 April 2010 (UTC)