Question

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

Answer 1

Hint: We check for each of the options whether they have factors other than 1 and the number itself and choose the smallest number that comes out to be a prime number.
* Any number is said to be a prime number if it has no other factors other than 1 and the number itself.

Complete step-by-step solution:
We know a prime number has only two factors i.e. it is divisible by either 1 or by the number itself.
We check each option separately.
Option A. 101
We know \[101 = 101 \times 1\]
But we cannot write 101 as a factor of any other number.
\[ \Rightarrow \]101 is a prime number
Option B. 103
We know \[103 = 103 \times 1\]
But we cannot write 103 as a factor of any other number.
\[ \Rightarrow \]103 is a prime number
Option C. 109
We know \[109 = 109 \times 1\]
But we cannot write 109 as a factor of any other number.
\[ \Rightarrow \]109 is a prime number
Option D. 113
We know \[113 = 113 \times 1\]
But we cannot write 113 as a factor of any other number.
\[ \Rightarrow \]113 is a prime number
So, all the numbers 101, 103, 109 and 113 are prime numbers.
We have to find the smallest 3-digit prime number from these given numbers.
As all are 3-digit numbers we will have to check whichever of the four numbers is the smallest in numeric value by comparing their position on the number line.
We know any number on the left hand side of the number line is always less than the number on the right hand side of the number line.
Since 101 lies in the leftmost on the number line, so 101 is the smallest number of all these four numbers.
\[\therefore \]101 is the smallest 3-digit prime number

\[\therefore \]Option A is correct.

Note: Many students make the mistake of ignoring the options with digit ‘0’ in between the number and consider only 113 as the option of 3-digit number. Keep in mind we ignore only that 3-digit number when the hundreds place has ‘0’ in it because then the number reduces to a 2-digit number.