# Prime and Composite Number

In our next tutorial, we are going to look at another interesting concept in mathematics, prime and composite numbers. Numbers can be generally classified into 2 categories namely prime and composite numbers.

A prime number is a number that is divisible only by itself and 1. Take for example, the following numbers, 1, 3,5,7,11,13,17… These numbers are not divisible by any other numbers except they are divisible only by 1 or the number itself. When it comes to prime numbers, the numbers 0 and 1 are not considered to be either prime or composite numbers. And any number that ends with 5 is divisible by 5 and hence is not a prime number.

A composite number is a number that is not basically a prime number and is divisible by either 1, itself or other numbers. In other words, if you can divide the number exactly, it is a composite number, whereas if the number cannot be divided exactly, it is a prime number. 1 is nor a prime number or a composite number.

Let’s describe the concept of prime and composite numbers with some examples:

Take for example, the numbers 3, 5 & 7

Number 3 is divisible by only 1 or itself. Hence, number 3 is a prime number. Similarly, other prime numbers like 5,7.
Take for example, 6 is a composite number, because it is divisible by 2 or 3

6 = 1 x 6
6 = 2 x 3

Hence, number 6 is a composite number.

One basic requirement for a prime number is that it should be an odd number but remember all odd numbers are not prime numbers. Take for example, 99 is an odd number, but is divisible by 1, 99 and 3 and many other numbers, hence not a prime number. Also, 2 is the only even number in the prime numbers’ list. All other even numbers are divisible by 2, hence they are not prime numbers either.

And we are only talking about whole numbers here, as we are not talking about dividing in decimal numbers. Hence any whole that is greater than 1 is either a prime or a composite number. In other words, if the only factors of that number are either 1 or itself, it is a prime number. Anything else if it has more factors other than 1 and itself, it is a composite number.

Example 1 – Is 10 a prime or composite number?

10 / 10 = 1
10 / 1 = 10
10 / 2 = 5
10 / 5 = 2

Since 10 is divisible by 1, 5, and 2, it is a composite number.

Example 2 – is 57 a prime or composite number?

57 / 57 = 1
57 / 1 = 57
57 / 7 = 8
57 / 8 = 7
57 / 3 = 19

57 is a composite number.

Example 3 – is 13 a prime or composite number?

13 / 13 = 1
13 / 1 – 13

Since 13 is not divisible by any other number besides itself and 1, it is a prime number.

### One Comment

1. Hundred Worries.Com May 27, 2020 at 2:07 pm - Reply

** From the given chart you can see the smallest prime number is 2 and the smallest composite number is 4.