divisibility rule for 6

Rule:
A number is divisible by 6,if it is divisible by both 2 and 3.
Example1:
Is 567894 divisible by 6?
Solution:
The unit digit in the number 567894 is 4.So by the divisibility rule for 2,the number 567894 is divisible by 2.
The sum of digits in 567894 is 39 which is divisible by 3.So by the divisibility rule for 3,the number 567894 is divisible by 3.
According to the rule given above,the number 567894 is divisible by 6.
Example2:
Is 782345 divisible by 6?
Solution:
The unit digit in the number 782345 is 5. So by the divisibility rule for 2,the number 782345 is not divisible by 2.
The sum of the digits in 782345 is 29 which is not divisible by 3. So by the divisibility rule for 3,the number 782345 is not divisible by 3.
As per the rule given above,the number 7823465 is not divisible by 6.