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Mental Math: A New Divisibility Rule for Three-Digit Numbers (and more!)

Photo by Mike Szczepanski on Unsplash

Any three digit number formed of consecutive digits is divisible by three.

  1. Assume the three digit number has the digits XYZ, where X, Y, and Z are consecutive.
  2. For the sake of convention, let’s represent X by n.
  3. Since the integers are consecutive, then Y = n + 1 AND Z = n + 2
  4. Notice that it does not matter whether the number is XYZ or YZX: it will not change the value.
  5. Add X, Y, and Z. You will get n + (n+1) + (n+2) = 3n+3
  6. Divide (3n + 3) by 3 and you will get n + 1, without any remainder. Since the sum is divisible by three, then the number is divisible by three. It is also shown that the order of the consecutive integers does not matter.



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