 # Composite Numbers

In Mathematics, composite numbers are numbers that have more than two factors. It is just the opposite of prime numbers which have only two factors, i.e. 1 and the number itself. These numbers are also called compositesAll the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers. For example, 6 is a composite number because it is divisible by 1, 2, 3 and even by 6.

## What is a Composite Number in Maths?

The integers which can be generated by multiplying the two smallest positive integers and contain at least one divisor other than number ‘1’ and itself are known as composite numbers. These numbers always have more than two factors.

Fact: Any even number which is greater than 2 is a composite number.

### Examples of Composite Numbers

The examples of composite numbers are 6, 14, 25, 30, 52, etc.

There are a number of composite numbers we can list out of set of natural numbers from 1 to 1000 or more. Let us see the list of composite numbers in the next section.

## List of Composite Numbers

Here is the list of composite numbers from 1 to 100 in Maths. Students can keep a note of this and also try to write the numbers beyond 100 for practice, such composites from 1 to 200 or till 500. ### Composite Numbers Up to 200

The positive integers having more than two factors are composite numbers. The list of Composite numbers from 1 to 200 are given below in the table.

 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, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150,  152, 154, 155, 156, 157, 158, 159, 160, 162, 164, 165, 166, 168, 170, 172, 174, 175, 176, 177, 178, 180, 182, 184, 185, 186, 187, 188, 189, 190, 192, 194, 195, 196, and 198.

### Is 0 a Composite Number?

Zero (0) is considered as neither prime nor a composite number because it do not have any factors.

## How to Determine the Composite Number?

The procedures to find whether a given number is prime or composite:

• Find all the factors of the positive integer
• A number is said to be prime if it has only two factors, 1 and itself.
• If the number has more than two factors, then it is a composite.

Example: Find if 14 is a composite number.

Let us find the factors of 14.

• 14÷1 = 14
• 14÷2 = 7
• 14÷7 = 2
• 14÷14 = 1

As we can see, the factors of 14 are 1,2,7 and 14, so it is a composite number.

## Properties of Composite Numbers

The properties of composite numbers are easy to remember.

• Composite numbers are evenly divisible by their factors
• Each composite number will include at least one prime number as its factor
• Composite numbers are divisible by other composite numbers also

## Types of Composite Numbers

There are two main types of composite numbers in Maths which are:

• Odd Composite Numbers or Composite Odd Numbers
• Even Composite Numbers or Composite Even Numbers

### Odd Composite Numbers

All the odd integers which are not prime are odd composite numbers. Examples of composite odd numbers are 9, 15, 21, 25, 27, 31, etc.

### Even Composite Numbers

All the even integers which are not prime are even composite numbers. Examples of even composite numbers are 4, 6, 8, 10, 12, 14, 16, etc.

## Smallest Composite Number

4 is the smallest composite number.

Why?

1 is not a composite number because the sole divisor of 1 is 1. The positive integers 2 and 3 are prime numbers because it can be divided by only two factors, one and itself. Hence 2 and 3 are not composite.

But in the case of number 4, we have more than two factors. The divisors of 4 are 1,2,4. So this number satisfies the condition of a composite number as mentioned above. After 4, 6 is the next composite positive integer, which has factors 1, 2, 3 and 6.

Hence, 4 is the smallest composite number (Proved).

 Important Notes: Smallest Composite Number = 4 Smallest Prime Number = 2 Smallest Odd Composite Number = 9 Two-digit Smallest Composite Number = 10

## Prime and Composite Numbers

The difference between the prime numbers and the composite numbers in Maths are listed below:

Prime Numbers Composite Numbers
It can only be divided by 1 and itself, thus have only two factors. It has more than two factors (1 and itself).
It can only be written as a product of two numbers It can be written as the product of two or more numbers
Example: 5 has factors are 1 and 5 Example: 4 has factors are 1, 2 and 4

## Prime Factorisation of Composite Numbers

The list of composite numerals from 1 to 50 are given here with their prime factorisation. You can see here how the composites are factorised in prime numbers. Check the below table to understand better. With the help of this table, you can also find composites beyond 50 with their prime factorisation.

 Composite Numbers Prime Factorisation 4 2 × 2 6 2 × 3 8 2 × 2 × 2 9 3 × 3 10 2 × 5 12 2 × 2 × 3 14 2 × 7 15 3 × 5 16 2 × 2 × 2 × 2 18 2 × 3 × 3 20 2 × 2 × 5 21 3 × 7 22 2 × 11 24 2 × 2 × 2 × 3 25 5 × 5 26 2 × 13 27 3 × 3 × 3 28 2 × 2 × 7 30 2 × 3 × 5 32 2 × 2 × 2 × 2 × 2 33 3 × 11 34 2 × 17 35 5 × 7 36 2 × 2 × 3 × 3 38 2 × 19 39 3  × 13 40 2 × 2 × 2 × 5 42 2 × 3 × 7 44 2 × 2 × 11 45 3 × 3 × 5 46 2 × 23 48 2 × 2 × 2 × 2 × 3 49 7 × 7 50 2 × 5 × 5

## Solved Examples

Q.1: Find if 328 is a composite number.

Solution: The factors of 328 are 1, 2, 4, 8, 41, 82, 164, 328.

Therefore, 328 is a composite number.

Q.2: What is the prime factorisation of 60?

Answer: The prime factorisation of 60 is:

60 = 2 × 2 × 3 × 5

### Practice Questions

1. List the composite numbers between 20 and 30.
2. Find if 85 is a composite number.
3. What are the prime factors of 99?

## Frequently Asked Questions – FAQs

### What is a composite number?

A composite number is a natural number or a positive integer which has more than two factors. For example, 15 has factors 1, 3, 5 and 15, hence it is a composite number.

### Is 2 a composite number?

No, 2 is not a composite number because it has only two factors, i.e. 1 and 2. Hence, it is a prime number.

### Is 9 a composite number?

Yes, 9 is a composite number because it has more than two factors, such as 1, 3 and 9.

### What are the composite numbers from 1 to 100?

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.

### Is 19 prime or composite?

19 is a prime number because it has only two factors, i.e. 1 and 19.

### Is 1 a composite number?

No, because 1 does not have more than two factors instead it has only 1 factor. Hence, it is neither prime nor composite.

### How many composite numbers are there between 1 and 10?

There are four composite numbers between 1 and 10. They are 4,6,8 and 9.

Test your knowledge on Composite Numbers