Question

What is the smallest odd prime? Is every odd number a prime number? If not, give an example of an odd number which is not prime.

Answer 1

Hint: You can write the first few odd numbers to check which is the smallest odd prime number. And also by checking the number of factors of these prime numbers. We can check whether all odd numbers are prime or not. If not then we will find a number which is odd but not prime.

Complete step-by-step answer:

Those numbers are said to be prime, which have only two factors namely ‘1’ and itself.

And odd numbers are those numbers which are not divisible by 2.

We have to find the smallest odd prime number. So, let us list the first ten odd numbers.

First ten odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

The smallest odd number is ‘1’. ‘1’ is neither a prime number nor a composite number by convention.

The next smallest odd number is ‘3’.

Factors of 3 = 1, 3.

There are only two factors of ‘3’- ‘1’ and ‘3’ (itself). So, ‘3’ is a prime number.

Hence, the smallest odd prime number is 3.

Now, let us check the number of factors of other prime numbers.

Let us take ‘9’. ‘9’ is not divisible by ‘2’. So, ‘9’ is an odd number.

Factors of 9 = 1, 3, 9.

‘9’ has more than two factors. So, it is not a prime number.

So, we can conclude that every odd number is not a prime number.

An example of an odd number which is not prime is - ‘9’. (As discussed above)

Note: Students can make mistakes by taking ‘1’ as the smallest odd prime number. But by convention ‘1’ is neither considered as a prime number nor a composite number. Prime numbers are defined to have exactly two factors and composite numbers are defined to be more than two factors. ‘1’ has only one factor -‘1’. So, it doesn’t follow the definition of either prime numbers or composite numbers and thus it is considered neither prime nor composite.