Question

What are composite numbers? Can a composite number be odd? If yes, write the smallest odd composite number.

Answer 1

Hint: We first need to define the term composite and then find the difference between prime and composite numbers. Then we discuss the relation of even and odd numbers with composite numbers. We find the smallest odd composite number.

Complete step by step answer:
The natural numbers can be broken into two parts according to their number of factors. The parts are prime and composite.
Prime numbers have only two divisors or factors and they are 1 and the number itself. Any other natural numbers other than prime are called composite numbers. Composite numbers have more than two factors.
For example: we take 6 and 7. 6 has four factors and they are 1, 2, 3, 6. So, 6 is a composite number. But 7 has only two factors and they are 1 and 7. So, 7 is a prime number.
Now we are going to talk about the odd and even numbers and them being prime or composite.
We know that the only even number which is also prime is 2. No other number can be both prime and even as they have at least 2 as their factor.
Similarly, it’s not necessary for a composite number to be even all the time as a composite number can have odd numbers as their factors. For example: we take 15. It’s a composite number as it has factors as 1, 3, 5, 15. There is no even number in its factor and 15 itself isn’t an even number. A composite number can be an odd number.
Let us consider numbers from 1 to 10 - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Here, 1 is not considered. 2, 4, 6 and 8 are even numbers, so can be avoided. 3, 5, 7 and 9 are odd numbers, out of which only 9 is a composite number since it has 3 as its factor.

Therefore, the smallest odd composite number is 9.

Note: We noticed that other than 9 there is no other odd composite number in the first 10 numbers. Either they are prime or even composite numbers. Although we mentioned natural numbers in time of defining things, we never could use the number 1 as it can’t have any other factor other than itself. So, we can’t place it in any of the definitions. 1 is neither composite nor prime. The common mistake the students commit is while writing the smallest odd composite number, they may write it as 3.