If a number is divisible by both 2 and 3, then it is divisible by 6.
We already know that all even numbers are divisible by 2.
So, all even numbers which are divisible by 3 are divisible by 6.
Example 1 :
Check whether 5832 is divisible by 6.
Solution :
The given number 5832 ends with 2.
So, it is even number and divisible by 2.
Check whether the number 5832 is divisible by 3.
Add all the digits.
5 + 8 + 3 + 2 = 18
The sum of the digits in the given number 5832 is 18 which is a multiple of 3.
Therefore, the given number 5832 is divisible by both 2 and 3.
So, the given number 5832 is divisible by 6.
Example 2 :
Check whether 7434 is divisible by 6.
Solution :
The given number ends with 4.
So, it is even number and divisible by 2.
Check whether the number 7434 is divisible by 3.
Add all the digits.
7 + 4 + 3 + 4 = 18
The sum of the digits in the given number 7434 is 18 which is a multiple of 3.
Therefore, the given number 7434 is divisible by both 2 and 3.
So, the given number 7434 is divisible by 6.
Example 3 :
Check whether 4538 is divisible by 6.
Solution :
The given number 4538 ends with 8.
So, it is even number and divisible by 2.
Check whether the number 4538 is divisible by 3.
Add all the digits.
4 + 5 + 3 + 8 = 20
The sum of the digits in the given number 4538 is 20 which is not a multiple of 3.
The given number 4538 is divisible by 2, but not by 3.
So, the given number 4538 is not divisible by 6.
Example 4 :
Check whether 1056 is divisible by 6.
Solution :
The given number 1056 ends with 6.
So, it is even number and divisible by 2.
Check whether the number 1056 is divisible by 3.
Add all the digits.
1 + 0 + 5 + 6 = 7
The sum of the digits in the given number 1056 is 7 which is a multiple of 3.
Therefore, the given number 1056 is divisible by 2, but not by 3.
So, the given number 1056 is not divisible by 6.
Example 5 :
Check whether 2105 is divisible by 6.
Solution :
The given number 2105 ends with 5.
So, it is not an even number and it is not divisible by 2.
Therefore, the given number 2105 is not divisible by 6.
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