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How to Find a Number Divisible by 7?

Published in Number Theory 2 mins read

To determine if a number is divisible by 7, you can use a simple trick:

  1. Remove the last digit of the number.
  2. Double the removed digit.
  3. Subtract the doubled digit from the remaining number.
  4. If the result is divisible by 7, then the original number is also divisible by 7.

Example:

Let's take the number 357:

  1. Remove the last digit (7).
  2. Double the removed digit (7 x 2 = 14).
  3. Subtract the doubled digit from the remaining number (35 - 14 = 21).
  4. 21 is divisible by 7, so the original number 357 is also divisible by 7.

Other methods:

  • Direct division: You can always divide the number by 7 and check if the remainder is zero.
  • Programming: You can use programming languages like Python to write a function that checks if a number is divisible by 7 using the modulo operator (%) which returns the remainder of the division.

In conclusion, the divisibility rule of 7 provides a quick and efficient way to determine if a number is divisible by 7 without performing actual division. This rule is based on the properties of modular arithmetic and can be applied to numbers of any size.

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