2

I know a few rules

  • number ends with even digit, it is divisible by 2
  • number ends with 5 or 0 is divisible by 5
  • if sum of all digits in a number is divisible by 3 then that number is divisible by 3

How many more rules are there for division?

rae306
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LifeH2O
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  • If your search here on "divisibility test" or "casting" you'll probably find more than you desire. Please try the obvious searches before posing a question. – Bill Dubuque Apr 08 '11 at 20:32
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    Only idea i had for searching was rules of division. I am not a mathematician to know all suitable keywords, i just asked it because i needed those rules for GRE – LifeH2O Apr 08 '11 at 20:41
  • Learning how to effectively perform searches is a fundamental internet skill. Here the keywords are obvious, requiring no specialized knowledge. Every obvious search I tried here, e.g. "division", "divisibility", "division rules" turned up many pertinent results on the first page of matches. Did you actually try any of these searches before posing your query? – Bill Dubuque Apr 08 '11 at 21:37
  • @LifeH2O: And what is GRE? – awllower Apr 09 '11 at 02:43
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    @Bill sorry for that, i only searched for one keyword and found no clear answer looking at question titles. Anyway does this question matter? I am sure it will help someone finding "rules of division". If this question should not be here you can surely flag it. I got what i was looking for. – LifeH2O Apr 09 '11 at 08:03
  • @awllower it is http://en.wikipedia.org/wiki/Graduate_Record_Examination – LifeH2O Apr 09 '11 at 08:04
  • Oh, I know it now, thanks very much, http://math.stackexchange.com/users/1515/lifeh2o. – awllower Apr 11 '11 at 11:52

3 Answers3

8

A lot

Divisibility Rules

GeoffDS
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    Every time I see a downvote, I see someone say, "Whoever downvoted, you should explain why." But, rarely is someone polite enough to do it ahead of time. – GeoffDS Apr 08 '11 at 20:39
  • Perhaps because the above should have been a comment - having no original content. – Bill Dubuque Apr 08 '11 at 20:50
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    @Bill Possibly, but I have never heard of such a rule. That's the reason a downvote with no explanation is worthless and rude. It doesn't teach me anything. Your comment was helpful though, so thanks. – GeoffDS Apr 08 '11 at 20:56
  • +1, I was tempted to down-vote because the motivation behind stackexchange-like sites -- at least, based on the FAQs I've read -- is to become something like Wikipedia, but designed in such a way to motivate people to more proactively contribute content. Wikipedia doesn't just contain external links, they actually provide content. If the link was to some message forum or some other site that didn't have a high likelihood of long-term survival, I probably would've down-voted. – Brian Vandenberg Apr 08 '11 at 21:06
  • @Bill - An answer is an answer. If original content was the requirement, most answers would be illegitimate because in most cases people would be quoting from, or regurgitating material from another source -- often without credit given. – Brian Vandenberg Apr 08 '11 at 21:08
  • @Numth: There are no "rules" on such. But the site would be quite sterile if it consisted merely of links to offsite content that could easily be located by obvious searches. Now that the OP has quickly accepted the above link, it highly reduces the likelihood that others will contribute insightful answers. Further, the Wikipedia article is horrible from a pedagogical standpoint - lending little conceptual insight on the essence of the matter. – Bill Dubuque Apr 08 '11 at 21:09
  • @Bill - That's an excellent point, but in this case the OP needed it for the GRE. One of the more frustrating things for me 'growing up' in math was trying to digest material in Mathworld and Wikipedia math entries -- mostly because they were loaded with math jargon I was unfamiliar with. If someone's studying for the GRE, they shouldn't have to know a lot of math jargon just to learn a couple of divisibility tests. – Brian Vandenberg Apr 08 '11 at 21:13
  • @Brian: Do you really think that "divisibility" is "math jargon"? Further searching here on "division" alone shows many pertinent results on the first page of matches. So the OP could have easily located all (s)he needed with the most obvious search. – Bill Dubuque Apr 08 '11 at 21:15
  • @Bill - No. You made a good argument for a more general treatment of the topic. I'm arguing that there should be a "simplified" treatment as well. My point about the math jargon was to make the point that it doesn't need to be only readable by someone who has a desire to invest themselves in math enough to understand the more general/rigorous treatment. – Brian Vandenberg Apr 08 '11 at 21:23
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    @Brian: Point taken. But the OP could have easily located the Wikipedia link and many other links at various levels if (s)he had simply typed in any of the obvious search terms here. Generally we expect questioners to have shown some effort before posing a question, lest the site degenerate into a "do my search please" site. – Bill Dubuque Apr 08 '11 at 21:27
  • @Bill - Well put. – Brian Vandenberg Apr 08 '11 at 21:30
8

All of these ad-hoc divisibility tests are absolutely trivial if you know congruence / modular arithmetic. For example, see my discussion of casting out $91$'s linked in my answer to a similar prior question.

Therefore, if you desire to obtain some universal insight into divisibility tests, I strongly recommend that you first learn modular arithmetic. It's a protypical example of a ubiquitous algebraic problem solving technique - modular reduction. Due to this generality, the time invested in this endeavor will provide great rewards in your future studies.

Community
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Bill Dubuque
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    And to begin with, the Disquisitiones Arithmeticae is a good one, it is truly ingenious and easy to learn(the first four chapters). – awllower Apr 09 '11 at 02:46
0

This site shows the rules all the way up to 12.

The Wikipedia page has them up to 20 and beyond 20.

Geremia
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