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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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    Oh, I know it now, thanks very much, http://math.stackexchange.com/users/1515/lifeh2o.2011-04-11

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A lot

Divisibility Rules

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    @Bill - Well put.2011-04-08
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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).2011-04-09
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This site shows the rules all the way up to 12.

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