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11 divisibility proof

  1. Feb 6, 2008 #1
    1. The problem statement, all variables and given/known data

    what is the test to to see if a number is divisible by 11 and prove it.

    3. The attempt at a solution

    If the alternating sum of a numbers digits is divisble by 11 then so is the number.

    I dont know how to prove it tho.
  2. jcsd
  3. Feb 6, 2008 #2


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    Do a simple case. Take a two digit number n. First digit a, second digit b. So n=a*10+b. Rewrite this as n=a*10+((b-a)+a)=a*10+a+(b-a). Now a*10+a is always divisible by 11 (why?). So if (b-a) is divisible by 11, then n is.
  4. Feb 6, 2008 #3
    because it equals 11a.

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