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The divisibility rule for 42 is

  • divisibility by 2, AND
  • divisibility by 3, AND
  • divisibility by 7.

Divisibility by 2 requires the number to be even. That means it must end in 0, 2, 4, 6 or 8.

Divisibility by 3 requires that the digital root of the number is divisible by 3. That is, the sum of the digits is divisible by 3. If the first sum is large, you can calculate the digital root of the digital root (and again, if necessary) and check that for divisibility by 3.

The divisibility rule for 7 is more difficult.

Take the last digit (units).

From the number formed by the remaining digit, subtract twice the last digit.

If the answer is divisible by 7 (including zero or negative numbers), then the original number is divisible by 7.

For large numbers, repeat the process to bring the number down to a manageable size.

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Q: What is the divisibility rule for 42?
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