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Divisibility of seven

Kapitoly: Divisibility by two, Divisibility by three, Divisibility by four, Divisibility of five, Divisibility of six, Divisibility of seven, Divisibility of eight, Divisibility of nine, Divisibility of ten, Divisibility of eleven, Divisibility of twelve

How do we find out that a whole number is divisible by seven? Well, it's a bit tricky and it's not as easy as other divisibility. We have more than one way. Probably the easiest is this. Let's have a number 574 that we want to find out if it's divisible by seven.

  1. We take the last digit first and multiply it by two, i.e. 4 · 2 = 8.
  2. Now we take all but the last digit of the original number, i.e., 57, and subtract the previous sum from that number, i.e., perform the calculation 57 − 8 = 49.
  3. If this result is divisible by seven, the original number is also divisible by seven. Since the number 49 is divisible by seven, the number 574 is also divisible by seven.

This procedure can be repeated several times if necessary. For example, is the number 3409 divisible by seven?

  1. In the first step, multiply the last digit by two 9 · 2 = 18.
  2. Now subtract 340 − 18 = 322.
  3. Since we don't know if 322 is divisible by seven, we continue.
  4. We multiply the last digit by two: 2 · 2 = 4.
  5. Subtract from the rest: 32 − 4 = 28.
  6. The number 28 is divisible by seven, so the number 3409 is divisible by seven.