Divisibility rule of 6, 12, and 14 with examples

Divisibility Rule of 6, 12, and 14 – with Examples

Let’s proceed with the divisibility rule of 6, 12, and 14 in this tutorial. These rules are important when attempting a competitive exam, school exams, college exams, and even in practical life.

You can learn more about the importance of the divisibility rules and the easy tricks to memorize these by following the instructions here.

divisibility rule of 6, divisibility rule of 12, divisibility rule of 14

Divisibility rule of 6

Testing the divisibility of a number by 6 might prove helpful as 6 is one of the basic digits of the numbers. It is recommended that you memorize divisibility rules for at least all numbers between 2 and 9.

The divisibility rule of 6 says that “A number is only divisible by 6 if it is divisible by both 2 and 3“. Follow the below steps to test for the divisibility by 6.

  1. Check if the number is divisible by 2 by following the divisibility rule of 2. If yes, proceed to another next step. If no, the number is not divisible by 6.
  2. Check if the number is divisible by 3 by following the divisibility rule of 3. If yes, then the number is divisible by 6. If no, the number is not divisible by 6.

Examples,

For a number 954,

The one’s place digit is 4 (multiple of 2), and 9+5+4 = 18 (multiple of 3), hence the number is divisible by both 2 and 3. So, we can say the number is also divisible by 6 and gives 159.

On the other hand, 729 can be divided by 3 but not by 2; hence, it is not divisible by 6.

Similarly, you can test for other numbers with this divisibility rule of 6.

Divisibility rule of 12

After discussing the divisibility rule of 6, let’s move forward with the divisibility rule of 12.

The divisibility rule of 12 states, “If a number is divisible by both 4 and 3, then the number is divisible by 12”.

Follow the below steps to test the divisibility by 12:

  1. Step 1: Check if the number is divisible by 4 by following the divisibility rule of 4. If yes, proceed to another next step. If no, the number is not divisible by 12.
  2. Step 2: Check if the number is divisible by 3 by following the divisibility rule of 3. If yes, then the number is divisible by 12. If no, the number is not divisible by 12.

Examples,

For a number 4068, it is divisible by 4 as the number formed by the last two digits is a multiple of 4 (68). And the sum of all digits, 4+0+6+8 = 18 is a multiple of 3, hence the number is also divisible by 12 and gives 339 upon division.

On the other hand, 2648 is divisible by 4 but not by 3; hence, 2648 is not divisible by 12.

It proves the divisibility rule of 12 for any number. With this rule, you can check for any other number (small or large).

Note: 4 and 3 multiply to get 12, and provide the way to test the divisibility for 12. In the same case, you can not use 6 and 2 to test the divisibility by 12. It is because both 6 and 2 are multiples of the same number. Hence, it is necessary for both the numbers not to have a common divisor.
Similarly, the same can be applied to test the divisibilities of other numbers such as 18 (2 and 9 can be used but not 3 and 6), 24 (8 and 3 can be used but not 6 and 4).

Divisibility rule of 14

The divisibility rule of 14 is similar to that of 12. You will need numbers that are divisors of 14 but do not have a common divisor. i.e., 2 and 7. Both are divisors of 14 but do not have a common divisor.

The divisibility rule of 14 states, “If a number is divisible by both 2 and 7, then the number is also divisible by 14”.

Follow the below steps to test the divisibility by 14 for any number:

  1. Step 1: Check if the number is divisible by 2 by following the divisibility rule of 2. If yes, proceed to another next step. If no, the number is not divisible by 14.
  2. Step 2: Check if the number is divisible by 7 by following the divisibility rule of 7. If yes, then the number is divisible by 14. If no, the number is not divisible by 14.

For example, let’s check the divisibility of 1288.

1288 is divisible by 2 as the last digit contains 8. It is also divisible by 7 as the difference between twice of unit digit and the remaining part is a multiple of 7, i.e., 128 – (2×8) = 116.

Hence, 1288 is divisible by 14 and gives 92 when divided.

I hope you have understood the above rules to test the divisibilities of numbers. You can practice these example questions to memorize all the divisibility rules mentioned above:

Q. Test the divisibility of the following numbers by 6, 12, and 14.

  • 15882
  • 3888
  • 3017
  • 9191928

Q. Write two numbers that are divisible by 6 and 14 but not 12.

Q. State true/false:

  • If a number is divisible by 12 that means it is also divisible by 6.
  • If a number is divisible by 6 then it is also divisible by 12.
  • 798 books can be divided into groups of 6 and 14 but can not be divided into groups of 12. Where each group has the same number of books.
  • While checking the divisibility of a number with 6, 14, or 12, the quickest option would be to check the divisibility by 2 first rather than checking for 3 or 7.

More Divisibility rules

Divisibility rule of 9Divisibility rules of 7
Divisibility rules of 25Divisibility rule of 19
Divisibility rule of 16
Divisibility rules table

I hope the above questions will help you practice the divisibility rule of 14, 12, and 6. You can check all the divisibility rules for numbers between 2 to 25 by following the links here.

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