# Rules of Division

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?

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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 8 '11 at 20:32
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 8 '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 8 '11 at 21:37
@LifeH2O: And what is GRE? –  awllower Apr 9 '11 at 2:43
@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 9 '11 at 8:03

A lot

Divisibility Rules

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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. –  Graphth Apr 8 '11 at 20:39
Perhaps because the above should have been a comment - having no original content. –  Bill Dubuque Apr 8 '11 at 20:50
@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. –  Graphth Apr 8 '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 8 '11 at 21:06
@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 8 '11 at 21:27

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.

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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 9 '11 at 2:46

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