Divisibility Test of 12

What is meant by the divisibility test of 12?

It is stated by the divisibility test of 12 that the whole number is divisible by 6 only if it is divisible by both 3 and 4. So, to check the number’s Divisibility by 12, it is vital to check if the same number is divisible by 3 and 4. 

Therefore, to better understand the divisibility test of 12 it is important to learn the divisibility rules of both 3 and 4.

• The divisibility test of 3:

It is stated by the divisibility rule of 3 that if the sum of the digits of a number is completely divisible by 3 then the original number will also be divisible by 3. 

For example, let’s take the number 563. Follow the mentioned procedure to check if the number is divisible by 3 or not:

1. Calculate the sum of the digits of the number 563 (5 + 6 + 3 = 14). 

2. Now that the sum of the digits of the given number is 14 check if it is divisible by 3.

3. 14 is not divisible by 3. It means that the given number 563 will also be not divisible by 3.

Now, for better understanding let us take one more example, 732. By summing up the digits of a given number 732 i.e. 7 + 3 + 2, we get 12. And, 12 is divisible by 3. It implies that the given number 732 will also be divisible by 3. 

• The divisibility test of 4:

It is stated by the divisibility rule of 4 that if the last two digits of the given number are either 00 or are divisible by 4 then the original number is said to be divisible by 4. For example, 540 is the given number having the last- two digits as 40 which are completely divisible by 4. On the other hand, 653 is another number having the last-two digits as 53 which are not divisible by 4. It means that the number 653 will also not be divisible by 4. 

Enlisting the steps to be followed to check whether the number 540 is divisible by 4 or not:

1. Take the last two digits of the number 540 which are 40 and divide it by 4.

2. If the last-two digits 40 are divisible by 4 then it means that the given number 540 will also be divisible by 4.

Now that you have understood the divisibility rules of 3 and 4, it’s time that you know about the divisibility test of 12.

Explaining the divisibility test of 12:

As discussed above, to check the number’s Divisibility by 12, it’s important to check if the number is divisible by both 3 and 4. Let’s know about the divisibility test of 12 with examples:

1. Applying divisibility test of 12 on the number 672: 

Condition 1: The number should be divisible by 3. When adding the digits of the number 672 (6 + 7 + 2 = 15), the sum obtained is 15 which is divisible by 3. Now that the sum of digits is divisible by 3, the number will also be divisible by 3.

Condition 2: The number should be divisible by 4. The last two digits of the given number 672 are 72 which are divisible by 4. Now that the last two digits are divisible by 4, the number will also be divisible by 4.

Thus, 672 satisfies both the conditions, i.e. it is divisible by 3 and 4. Therefore, it can be said that 672 is divisible by 12. 

2. Applying divisibility test of 12 on the number 964:

Condition 1: The number should be divisible by 3. When adding the digits of the number 964 (9 + 6 + 4 = 19), the sum obtained is 19 which is not divisible by 3. Now that the sum of digits is not divisible by 3, the number will also be divisible by 3.

Condition 2: The number should be divisible by 4. The last two digits of the given number 964 are 64 which are divisible by 4. Now that the last two digits are divisible by 4, the number will also be divisible by 4.

Thus, 964 just satisfies one condition, i.e. it is divisible by only 4. Therefore, it can’t be said that 964 is divisible by 12. 

3. Applying divisibility test of 12 on the number 8743:

Condition 1: The number should be divisible by 3. When adding the digits of the number 8743 (8 + 7 + 4 + 3 = 22), the sum obtained is 22 which is not divisible by 3. Now that the sum of digits is not divisible by 3, the number will also be not divisible by 3.

Condition 2: The number should be divisible by 4. The last two digits of the given number 8743 are 43 which are not divisible by 4. . Now that the last two digits are not divisible by 4, the number will also be not divisible by 4.

Thus, 8743 does not satisfy both the conditions, i.e. it is divisible by 3 and 4. Therefore, it can’t be said that 8743 is divisible by 12.

Conclusion

The reason why divisibility rules are formulated by the mathematician is to cut short the original division process. The time given to solve the questions in the competitive exams is limited making it difficult for the candidates to solve mathematic questions using original long methods. Therefore, they look for the tricks as mentioned in the Vedic Maths to solve division-related questions. It is imperative for the aspirant preparing for the SSC exam to know the divisibility test of 12 to easily and quickly solve the related questions.