Question

Smallest \[\;6\] digit number divisible by \[\;6\]is ___________.
A. \[100000\]
B.\[100002\]
C. \[100003\]
D.\[100004\]

Answer 1

Hint: First of all apply the divisibility rule of \[2\]. Then apply the divisibility rule of \[3\] in such a way that the number is smallest. We should know the rule of divisibility by \[\;2\],\[\;3\] and \[\;6\].

Complete step-by-step answer:
Number should be divisible by\[\;6\] to be as small as possible.
For a number to be divisible by $ 6 $ the rule is that the number must be divisible by both $ 2 $ and $ 3 $ . The divisibility rule of $ 2 $ says that the unit digit of the number is even if the number is divisible by $ 2 $ .
So, only three choices are left $ 100000 $ , $ 100002 $ and $ 100004 $ . The divisibility rule for a number to be divisible by $ 3 $ is that the sum of the digits must be divisible by $ 3 $ . The sum of the digits for the number $ 100000 $ is $ 1 $ which is not divisible by $ 3 $ , the sum of the digits for the number $ 100002 $ is $ 3 $ which is divisible by $ 3 $ and the sum of the digits of the number $ 100004 $ is $ 5 $ which is not divisible by $ 3 $ .
So, we are left with only one number $ 100002 $ which is divisible by $ 6 $ .
So, the correct answer is “Option B”.

Note: In this type of question we need to take care of the many things and some of them are mentioned here which will be really helpful to understand the concept:
We need to use correct formula in such a way that solution does not become too complex
We should know the rule of divisibility by \[\;2\],\[\;3\] and \[\;6\].