# Prime and Composite Numbers

**Prime and composite numbers** are the two types of numbers, that differ based on the number of factors they have. A prime number is the one that has only two factors and a composite number has more than two factors. A factor is a value, that can divide a number or an expression evenly. In this lesson, the properties of prime numbers and composite numbers are given along with their difference, examples and tables. The chart of prime and composite numbers, given in this article, will help to identify them easily.

## What are Prime Numbers and Composite Numbers?

A prime number is a number which has exactly two factors i.e. ‘1’ and the number itself. A composite number has more than two factors, which means apart from getting divided by 1 and the number itself, it can also be divided by at least one positive integer. 1 is not a prime or composite number. Apart from these two, there is also a similar category of numbers which are coprime numbers. A detailed explanation of these numbers is given below.

### Prime Numbers

A prime number is the one which has exactly two factors, which means, it can be divided by only “1” and itself. But “1” is not a prime number.

**Example of Prime Number**

3 is a prime number because 3 can be divided by only two number’s i.e. 1 and 3 itself.

- 3/1 = 3
- 3/3 = 1

In the same way, 2, 5, 7, 11, 13, 17 are prime numbers.

### Composite Numbers

A composite number has more than two factors, which means apart from getting divided by the number 1 and itself, it can also be divided by at least one integer or number. We don’t consider ‘1’ as a composite number.

**Example of Composite Number**

12 is a composite number because it can be divided by 1, 2, 3, 4, 6 and 12. So, the number ‘12’ has 6 factors.

- 12/1 = 12
- 12/2 =6
- 12/3 =4
- 12/4 =3
- 12/6 =2
- 12/12 = 1

### Types of Composite Numbers

There are two types of composite numbers:

- Even composite numbers
- Odd composite numbers

### Odd Composite numbers

The odd positive integers or the odd numbers that are not prime numbers are called odd composite numbers. For example, 9, 21, 33, 45, etc., are odd composite numbers.

### Even Composite numbers

The even numbers that are not prime numbers are called even composite numbers. For example, 4, 10, 16, 28, 56, etc., are even composite numbers.

### What are Coprime Numbers?

The coprime-numbers or mutually primes or relatively primes are the two numbers which have only one common factor, which is 1. Let us understand the concept with an example.

Suppose there are two numbers, 14 and 15. Find whether both are coprime or not.

- The factors of 14 are 1, 2 and 7
- The factors of 15 are 1, 3 and 5.

For both the numbers, we can see, the common factor is 1. Therefore, 14 and 15 are coprime numbers. But if we consider another number say, 21, whose factors are 1, 3 and 7. Then, 21 is neither a coprime for 14 nor for 15.

### Smallest Composite Number

As you have understood already about the composite number, now let us know the smallest number which is composite in nature. If we see the list of composite numbers, it starts from 4, 6, 8, 9, 10, 12, 14, 15, and so on. So you can see here 4 is the smallest number, which has factors apart from 1 and itself, such as;

Factors of 4 are 1, 2, and 4.

## Prime and Composite Numbers List

The list of prime numbers from 1 to 100 are:

2 | 3 | 5 | 7 | 11 |

13 | 17 | 19 | 23 | 29 |

31 | 37 | 41 | 43 | 47 |

53 | 59 | 61 | 67 | 71 |

73 | 79 | 83 | 89 | 97 |

The list of composite numbers from 1 to 100 are:

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100 |

## Prime and Composite Numbers Chart

Identify the number of prime numbers given in the chart below and also with the help of this table, students can identify the list of composite numbers from 1 to 100.

**Note: **Numbers highlighted in yellow colour, are prime numbers while others are composite numbers.

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

## How to find if a number is prime or composite?

There are a few tricks and methods to remember if a given number is a prime or a composite number. We can use division method and Divisibility Rules to find if a number is divisible by one or more number. Also we have prime factorisation method to find the prime factors of composite numbers. Let us find out:

- If a number is divisible by another number (other than 1), then it is a composite number
- Any even number greater than 2 is a composite number
- A number greater than 2 and multiple of 2 is not a prime number but a composite number
- In the same way, multiples of any number other than 1, are not a prime number
- If the prime factorisation results in the product of two or more prime numbers, then it is a composite number
- We can use divisibility rules to check if a number is divisible by any other number or not

## Related Articles

- Composite Numbers
- Prime Numbers
- Prime Numbers from 1 to 1000
- Prime Factorization
- Prime Factors
- Difference between Prime, Composite And Even, Odd Numbers
- Co-Prime Numbers
- How to Find Prime Numbers?

## Solved Examples on Prime and Composite Numbers

**Q.1: Find if 81 is a prime number or composite number.**

Solution: Given, the number is 81

Since, it is an odd number, thus we can check dividing 81 by the smallest odd prime number, i.e., 3

81/3 = 27

Again 27 is an odd number, dividing it by 3, we get;

27/3 = 9

9 is an odd number and divisible by 3

9/3 = 3

And 3 is the factor of itself.

3/3/ = 1

Hence, 81 is divisible by 3, 9, 27, and 81. Thus, it is a composite number.

**Q.2: Is 127 a prime or composite number?**

Solution: Since 127 is an odd number, it is not divisible by 2

By the divisibility rule of 3, if the sum of digits of a number is divisible by 3, then the number is also divisible by 3.

127: 1 + 2 + 7 = 10

10 is not divisible by 3

127 is not divisible by 5 (since the unit place digit is not 0 or 5)

127 is not divisible by 7 (127/7 = 18.1425…)

127 is not divisible by 11 (127/11 = 11.5454…)

In the same way, we can check to divide 127 by other prime numbers such as 13, 17, 19,…

At the end, we will find that 127 is not divisible by any other number apart from 1 and 127 itself.

Hence, 127 is a prime number.

Students can also practise by creating charts for prime and composite numbers from 1 to 1000.

## Practise Question

- Find if 89 is a prime number or composite number.
- What are the factors of 9?
- What is the prime factorisation of 36?
- Which of the following is a prime number?
- 6
- 19
- 27
- 63