Talk:Greatest common divisor

message: Consider to add the following equation, for finding gcd for more than two given numbers, the following example is for given 3 numbers.
:\operatorname{gcd}(a,b,c)=
\operatorname{gcd}(\operatorname{gcd}(a,b),c)=
\operatorname{gcd}(a,\operatorname{gcd}(b,c)).  — Preceding unsigned comment added by Eido95 (talk • contribs) 18:15, 10 November 2018 (UTC)
replies: text: —Anita5192 (talk) 18:33, 10 November 2018 (UTC)
thread_title:  Equation for finding gcd for more than 2 numbers, this is an example for 3 numbers 

message: An editor has asked for a discussion to address the redirect Greatest common denominator. Please participate in the redirect discussion if you wish to do so.  D.Lazard (talk) 14:46, 31 March 2020 (UTC)
thread_title:  "Greatest common denominator" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Isn't there a name for the set comprising a number's prime factors (e.g., the two sets shown in the Venn diagram of in the "Using prime factorizations" subsection)?  I see nothing in the various prime/composite-related articles.  BMJ-pdx (talk) 14:37, 26 July 2021 (UTC)
replies: text: "The prime divisors of " is a phrase that is commonly considered as convenient. Not all sets needs to be named, and using too much set theory leads to pedantry. Compare " is a prime divisor of " and " is a member of the set of the prime divisors of ". Both sentences are correct, but the second one requires to know what is a set in mathematics, and what is a member of a set. Note that the concept of set is less than 150 years old, while the concept of prime divisor is more than 2000 years old. D.Lazard (talk) 15:12, 26 July 2021 (UTC)
replies: text:  My motivation came from how simple a definition of GCD could be with a simple name for such:  "GCD is the product of the members of the intersection of ..." (much simpler still in symbolic form).  Also, it could be used in a relatively simple proof that the square root of 2 (et. al) is irrational.  Granted, all possible without a nice terse name.  BMJ-pdx (talk) 15:48, 3 August 2021 (UTC)

text: "the two sets shown in the Venn diagram of in the "Using prime factorizations" subsection": This Venn diagramm does not show any set, but multisets, as there are repeated elements in them, which is not possible for sets. Another example that using set theory when it is not needed may be confusing. D.Lazard (talk) 16:10, 3 August 2021 (UTC)
replies: text:  I stand corrected.  However, I don't share your apparent disdain of set theory :-)  (As an aside, introduction to set theory was a feature of the "New Math" that started to be taught in the 1960's, and was musically satirized by mathematician Tom Lehrer.)  BMJ-pdx (talk) 16:38, 3 August 2021 (UTC)
thread_title:  Name for a number's set of prime factors? 

message: An editor has identified a potential problem with the redirect :Grootste gemene deler and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 13#Grootste gemene deler until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  ~~~~User:1234qwer1234qwer4 (talk) 02:40, 13 February 2022 (UTC)
thread_title:  "Grootste gemene deler" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Let a and b be distinct natural numbers. Then 
gcd(a, b) =gcd(|a-b|, min(a, b)) 202.168.85.234 (talk) 05:04, 13 June 2022 (UTC)
thread_title:  Euclid's algorithm principle 

message: The section Using prime factorizations begins with this:
"''
Greatest common divisors can be computed by determining the prime factorizations of the two numbers and comparing factors. For example, to compute , we find the prime factorizations 48 = 24 · 31 and 180 = 22 · 32 · 51; the GCD is then 2min(4,2) · 3min(1,2) · 5min(0,1) = 22 · 31 · 50 = 12 The corresponding LCM is then
2max(4,2) · 3max(1,2) · 5max(0,1) = 
24 · 32 · 51  = 720."
But the formulas for GCD and LCM of two integers are very important in number theory. 
There's nothing wrong with examples, but:
Why not just state the general formulas for GCD and LCM instead of solely giving examples???
I hope someone knowledgeable about this subject can fix this.
The the dismissive last sentence of this section:
"In practice, this method is only feasible for small numbers, as computing prime factorizations takes too long"
is wholly inappropriate since "practice" means entirely different things — especially in a case like this — to pure mathematicians as compared with applied mathematicians.
I hope someone knowledgeable about this subject can fix this, too. 2601:200:C082:2EA0:19F5:EB17:C336:8B35 (talk) 05:13, 18 March 2024 (UTC)
thread_title:  Why not state the (extremely simple) formulas in generality? 

message: I was surprised to see in the edit history that the abbreviation HCF had been removed from the article. It's very common here in the UK, as a quick web search reveals, though I wouldn't like to say whether it's more or less common than GCD. (When I see GCD, I have to remind myself that it's a synonym for HCF.)
It was clumsily introduced in the article, and doesn't need actually using in the text, but I think its existence needs at least mentioning. Maybe it's less common among academic mathematicians than the general public—I've no idea—but it's a term I think plenty of readers will be familiar with and indeed be looking up when they land on this article. Musiconeologist (talk) 00:43, 3 April 2024 (UTC)
thread_title:  HCF (abbreviation)