Question

Write the smallest odd prime number.

Answer 1

Hint: We use the definition of odd numbers and prime numbers and choose the smallest number (Positive number) that fits into the definition of both odd number and prime number.
* Any number is said to be a prime number if it has no other factors other than 1 and the number itself.
* A number is said to be an odd number if it can be represented in the form \[2n + 1\].

Complete step-by-step answer:
We have to find the value of the smallest odd prime number.
This means we have to find the smallest number which is a prime number and is odd.
Since we know the difference between an odd number and even number is that odd number can be written in the form of \[2n + 1\] and even number can be written in the form \[2n\].
\[ \Rightarrow \]The number will be of the form \[2n + 1\]............… (1)
Now we have to choose a number i.e. a prime number. Since we know from the definition of prime number that a prime number has no other factor than 1 and the number itself.
We write a few prime numbers in ascending order.
\[2,3,5,7,11...\]
Since the first prime number is 2.
\[ \Rightarrow 2 = 2 \times 1 + 0\].................… (2)
We check if it is an odd number. From equation (1) an odd number is of the type \[2n + 1\].
Also, from equation (2), we cannot write the number 2 in terms of an odd number.
\[ \Rightarrow \]2 is not an odd number.
Now from the list of prime numbers, we check the next number i.e. 3.
\[ \Rightarrow 3 = 2 \times 1 + 1\]................… (3)
We check if it is an odd number. From equation (1) an odd number is of the type \[2n + 1\].
Also, from equation (3), we can write the number 3 in terms of an odd number.

\[\therefore \]3 is the smallest odd prime number.

Note: Students are likely to make the mistake of writing the smallest prime number as 1. Keep in mind that 1 is an odd number but it is not a prime number. 1 is neither a prime nor a composite number. Any number which is not prime can be stated as a composite number.