DIVISIBILITY RULE

A divisibility rule is a quick and easy method to determine if a number is divisible by another number without actually performing the division.

Here are some common divisibility rules:

  • Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
  • Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
  • Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
  • Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
  • Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
  • Divisibility by 7: One divisibility rule for 7 is to take the last digit of the number, double it, and then subtract it from the rest of the number. If the result is divisible by 7, then the original number is also divisible by 7. This process can be repeated until a number is obtained that is clearly divisible by 7.
  • Divisibility by 8: A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
  • Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
  • Divisibility by 10: A number is divisible by 10 if its last digit is 0.
  • Divisibility by 11: One divisibility rule for 11 is to take the alternating sum of the digits (i.e., subtract the second digit from the first, add the third digit, subtract the fourth digit, and so on). If the result is divisible by 11, then the original number is also divisible by 11.
  • Divisibility by 12: A number is divisible by 12 if it is divisible by both 3 and 4.
  • Divisibility by 13: One divisibility rule for 13 is to take the last digit of the number, multiply it by 4, and add it to the rest of the number. If the result is divisible by 13, then the original number is also divisible by 13. This process can be repeated until a number is obtained that is clearly divisible by 13.
  • Divisibility by 14: A number is divisible by 14 if it is divisible by both 2 and 7.
  • Divisibility by 15: A number is divisible by 15 if it is divisible by both 3 and 5.
These rules can be helpful when performing mental calculations or when checking if a number is divisible by another number without performing the actual division. However, they are not foolproof and may not work in all cases.