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Divisibility Shortcuts

Check divisibility by 3, 9 or 11 without doing the actual division

The Rule

  1. 1For 3 or 9: add up all the digits. The remainder when dividing by 3 or 9 is the same as the digit sum's remainder.
  2. 2For 11: add and subtract digits alternately from the right. The remainder when dividing by 11 matches this alternating sum's remainder.