# Prime Numbers and Composite Numbers

Prime Numbers

Prime number is a natural number, which is greater than 1 and does not has any positive divisors other than 1 and the number itself
In other words, we can say prime numbers don’t have any factor other than 1 and the number itself.

Composite Numbers

Composite numbers are those numbers which are divisible by one or more numbers, other than 1 and the number itself.
In other words, we can say that numbers having more than two factors are composite numbers.

## Prime Numbers and Composite Numbers

### Examples of Prime Numbers

Question 1

Which of the following is a prime number?
10, 3, 4, 9

Explanation

Prime number is a natural number, which is greater than 1 and does not has any positive divisors other than 1 and the number itself
In other words, we can say prime numbers don’t have any factor other than 1 and the number itself.
Factors of 10 are 5 x 2
Factors of 3 are 3 x 1
Factors of 4 are 2 x 2
Factors of 9 are 3 x 3
Here, Factors of 3 are 3 x 1
3 is not divisible by any other number, other than 1 and itself
therefore, 3 is a prime number.

Question 2

Which of the following is a prime number?
14, 18, 24, 7

Explanation

Prime number is a natural number, which is greater than 1 and does not has any positive divisors other than 1 and the number itself
In other words, we can say prime numbers don’t have any factor other than 1 and the number itself.
Factors of 14 are 7 x 2
Factors of 18 are 3 x 3 x 2
Factors of 24 are 3 x 2 x 2 x 2
Factors of 7 are 7 x 1
Here, Factors of 7 are 7 x 1
7 is not divisible by any other number, other than 1 and itself
therefore, 7 is a prime number.

### Examples of Composite Numbers

Question 1

Which of the following is a composite number?
2, 6, 3, 5

Explanation

Composite numbers are those numbers which are divisible by one or more numbers, other than 1 and the number itself.
In other words, we can say that numbers having more than two factors are composite numbers.
Factors of 2 are 2 x 1
Factors of 6 are 2 x 3
Factors of 3 are 3 x 1
Factors of 5 are 5 x 1
Here, Factors of 6 are 2 x 3
6 is divisible by 2 , 3 , 1 , 6
Factors of 6 are 2 , 3 , 1 , 6
therefore, 6 is composite number.

Question 2

Which of the following is a composite number?
12, 7, 13, 11

Explanation

Composite numbers are those numbers which are divisible by one or more numbers, other than 1 and the number itself.
In other words, we can say that numbers having more than two factors are composite numbers.
Factors of 12 are 3 x 2 x 2
Factors of 7 are 7 x 1
Factors of 13 are 13 x 1
Factors of 11 are 11 x 1
Here, Factors of 12 are 3 x 2 x 2
12 is divisible by 3 , 2 , 1 , 6 , 4 , 12
Factors of 12 are 3 , 2 , 1 , 6 , 4 , 12
therefore, 12 is composite number.