Question

Find the smallest three-digit number divisible by 2 as well as 3.

Answer 1

Hint: Use the divisibility rule of 2 and 3 to determine which type of numbers are divisible by them. Start from the smallest three digit number and proceed one-by-one to check whether the selected number is divisible by 2 and 3 or not.

Complete step-by-step answer:

The divisibility rule of 2 states that any even integer is divisible by 2. Any number having the last digit as 0, 2, 4, 6 or 8 will be divisible by 2. If the number is odd then it will not be divisible by 2.

The divisibility rule of 3 states that, if we are provided with a number then we have to add all the digits of the number, and if this sum is divisible by 3 then the given number will also be divisible by 3.

Now, we come to the question. We have to find the smallest three digit number which is divisible by both 2 and 3. First of all the smallest three digit number is 100. We can see that 100 is divisible by 2 but the sum of the digits of this number is 1 which is not divisible by 3, hence, 100 is not the answer. Now, we come to the next number that is 101, since this number is odd therefore it is not divisible 2 and it is not our answer. Proceeding further we have 102. This is an even number and the sum of its digits is 3 which is divisible by 3 and therefore, it is divisible by both 2 and 3.

Hence, 102 is the smallest number which is divisible by 2 and 3 both.

Note: One thing we can note here is that when any number is divisible by both 2 and 3 then that number is divisible by 6 also, this is the divisibility rule of 6. Indirectly we are using this rule here. We can see that 102 is also divisible by 6.