Divisibility Test of 6

What is meant by the divisibility test of 6?

The divisibility test of 6 states that the whole number is divisible by 6 only if it is divisible by both 2 and 3. Therefore, to check the number’s divisibility by 6 it is important to check if the number is divisible by both 2 and 3.

So, let us learn the divisibility test of 2 and 3 to better understand the divisibility test of 6. 

• The divisibility test of 2: 

This specific rule states that in case a number is even or the last digit of the number is even i.e. the number has the last digit as 0, 2, 4, 6, and 8 then it will be completely divisible by 2. 

For example, 454 is an even number having the last digit as an even number (4) and thus, is completely divisible by 2. On the other hand, 567 is not an even number as the unit digit is odd (9) and thus, is not divisible by 2. 

Mentioning the steps to check whether the number 454 is divisible by 2 or not:

1. Take the last digit of the number 454 which is 4 and divide it by 2.

2. If the last digit 4 is divisible by 2 then it implies that the entire number 454 will also be divisible by 2.

• The divisibility test of 3:

This specific rule states that in case the sum of the digits of a number is completely divisible by 3 then the entire original number will also be completely divisible by 3. 

For example, consider the number 409. To check if the number is divisible by 3 or not follow the mentioned procedure:

1. Take the sum of the digits of the given number (4 + 0 + 9 = 13). 

2. Now that you have the sum, check if it is divisible by 3.

3. Here, the sum 13 is not divisible by 3. It implies that the number 409 will also not be divisible by 3.

Now let’s take another example, 351. By adding the digits of this number i.e. 3 + 5 + 1, the sum obtained is 9. And 9 is completely divisible by 3. It means that the number 351 will also be divisible by 3. 

Now that you have understood the divisibility rule of both 2 and 3 it’s time to learn about the divisibility test of 6. 

Stating the divisibility test of 6:

As discussed above, to check the number’s divisibility by 6, it’s essential to check if the number is divisible by both 2 and 3. Let’s understand the divisibility test of 6 with examples:

1. Applying divisibility rule of 6 on the number 3594:

Condition 1: The number must be divisible by 2. Now that the mentioned number 3594 ends with an even digit 4, it is divisible by 2. It implies that the entire number 3594 is also divisible by 2. 

Condition 2: The number must be divisible by 3. Now that the sum of the mentioned number 3594 is 21 (3 + 5 + 9 + 4 = 21), it is divisible by 3. It implies that the entire number 3594 is also divisible by 3.

Thus, 3594 fulfills both the conditions, i.e. it is divisible by 2 and 3. Hence, it can be said that 3594 is divisible by 6. 

2. Applying divisibility rule of 6 on the number 6543:

Condition 1: The number must be divisible by 2. Now that the mentioned number 6543 ends with an odd digit 3, it is not divisible by 2. It implies that the entire number 6543 is not divisible by 2. 

Condition 2: The number must be divisible by 3. Now that the sum of the mentioned number 6543 is 18 (6 + 5 + 4 + 3 = 18), it is divisible by 3. It implies that the entire number 6543 is also divisible by 3.

Thus, 6543 fulfills only one condition, i.e. the number is divisible by 3. Hence, it can’t be said that 6543 is divisible by 6. 

3. Applying divisibility rule of 6 on the number 9865:

Condition 1: The number must be divisible by 2. Now that the mentioned number 9865 ends with an odd digit 5, it is not divisible by 2. It implies that the entire number 9865 is not divisible by 2. 

Condition 2: The number must be divisible by 3. Now that the sum of the mentioned number 9865 is 28 (9 + 8 + 6 + 5 = 28), it is not divisible by 3. It implies that the entire number 9865 is also not divisible by 3.

Thus, 9865 does not fulfill any condition, i.e. the number is not divisible by 2 as well as 3. Hence, it can’t be said that 9865 is divisible by 6.

Conclusion

The divisibility rules are formulated by the mathematician to make it easy and quick to solve the questions related to the division. Now that the time duration in competitive exams like SSC is limited, the candidates need to look for the tricks to solve the questions quickly and accurately. An aspirant aspiring to score a decent rank in the SSC exam must be aware of the divisibility test of 6. Here this article will help the candidates to learn all about the divisibility rule of 6.