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Greatest common divisor 
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#1
Jun2913, 02:43 AM

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Are there any real life applications of the greatest common divisor of two or more integers?



#2
Jun2913, 03:08 AM

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Yes. i.e. whenever you have something depending on a ratio ...
It's not normally expressed in that way though. Mostly  the lesson is important for the practise it gives in a kind of problem solving. 


#3
Jun2913, 03:15 PM

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There are a whole bunch. I use the idea regularly so it is difficult to point to a specific thing...



#4
Jun2913, 10:58 PM

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Greatest common divisor



#5
Jun3013, 12:04 AM

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Here take a look at this Wikipedia article.
https://en.wikipedia.org/wiki/Euclidean_algorithm Besides all the mathematical applications, I'm sure that you must sometimes call upon the GCD when shopping or possibly even cooking. 


#6
Jun3013, 04:29 AM

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wiki_inverse_in_finite_field.htm 


#7
Jun3013, 07:15 AM

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GCD is used any time you want to simplify integers, but have the same ratios as the others have said. Another way to say it is the numbers scale equally. An example is in solving empirical formulas, where you reduce all integers in a chemical formula. Such as hexane C6H8 > C3H4 GCD(6,8) is 2 so divide each by 2 to get the answer. Though it isn't of much use, but it has a name.



#8
Jul813, 01:58 PM

P: 235

The store sells 8packs of hotdogs and 12packs of buns. If you want the same (nonzero) number of each, what's the cheapest way to do it?



#9
Jul913, 12:51 AM

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@economicsnerd: good example, well done!
Most people wouldn't do that by listing the divisors, but I suppose there are examples less amenable to a bit of trial and error. Do HS math text books no longer have examples like that these days? 


#10
Jul913, 03:16 AM

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#11
Jul913, 12:19 PM

P: 235

Computing either the GCD or the LCM would get you close to knowing how many bags of each to buy. You either compute {h/GCD(h,b), b/GCD(h,b)} or {LCM(h,b)/h, LCM(h,b)/b}. 


#12
Jul913, 03:55 PM

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If you can think of a real life application of linear Diophantine equations, then the GCD and the Euclidean algorithm have applications to solving those.



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