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Math Help - Divisiblity test for 3

  1. #1
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    Divisiblity test for 3

    If a number is divisible by 3 then if the sum of its digits is divisible by 3.

    Why is this true. I know it has something to with modulus...

    Please show.

    I'm asking because I don't want to just memorize each rule, I wan to be able to just figure it out...
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  2. #2
    Super Member Bacterius's Avatar
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    Hello,
    you might want to look at this website that pretty much explains it all nicely :

    Math Forum: Explaining the Divisibility Rules

    It is really a property of our positional notation system.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jzellt View Post
    If a number is divisible by 3 then if the sum of its digits is divisible by 3.

    Why is this true. I know it has something to with modulus...

    Please show.

    I'm asking because I don't want to just memorize each rule, I wan to be able to just figure it out...
    I don't think Bacterius's link used modulus. For that merely note that every number may be represented in the form a_0+10a_1+\cdots+10^n a_n. So, noticing that 10\equiv 1\text{ mod }3 we see that a_0+10a_1+\cdots+10^na_n\equiv a_0+a_1+\cdots+a_1\text{ mod }3 from where the conclusion follows immediately.
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