Question

The smallest 3 digit prime number is
A.101
B.103
C.109
D.113

Answer 1

Hint: If the number is a prime number then it will be having only two factors i.e. 1 and the number itself and also it won’t be divisible by any of the prime numbers 2, 3, 5, 7…. Here, to show that a number is prime, check whether the unit digits is not divisible by 0, 2, 4, 6 and 8 sum of the digits is not divisible by 3 and the number is not divisible by prime numbers below its square root.

Here, we have to find the smallest 3 digit prime number.
We know that the smallest 3 digit number is 100. First, we have to check whether it is prime or not.
We know that a prime number is a whole number which has only two factors 1 and itself.
To check whether a number is prime or not, we have to check the following steps:
Check whether the unit digit is divisible by 0, 2, 4, 6 and 8. If it is divisible then it is not a prime number
Consider the sum of the given number, if it is divisible by 3, then it is not a prime number.
If the first two steps turn false, then take the square root of the number.
If it is a perfect square then take its square root again.
Divide the given number by all the prime numbers below its square root.
If the number is divisible by any of the prime numbers less than its square root, it is not a prime number, otherwise it is a prime.
 Now consider 100, clearly 100 is divisible by 2, i.e. $\dfrac{100}{2}=50$. Therefore 100 is not a prime number.
Now consider 101, now by according to steps:
The unit place of 101 is 1, which is not divisible by 0, 2, 4, 6 and 8.
Consider the sum of the digits of 101 which is, 1+0+1=2, 2 is not divisible by 3.
Consider the square root of 101 i.e. $\sqrt{101}<11$. Now take the prime numbers below 11 which are 2, 3, 5 and 7.
Clearly we can say that 101 is not divisible by the prime numbers 2, 3, 5 and 7.
Hence, we can say that 101 is a prime number.
Therefore, the smallest 3 digit prime number is 101.
Hence, the correct answer for this question is option (a).

Note: For smaller numbers we check if the number is prime or not by prime factorisation. If it is getting more than 2 factors then it is not a prime number. But for larger numbers follow the steps. Here, for 101 we followed the steps, which made the evaluation much easier.