# Composite Numbers

Composite numbers are those natural numbers greater than 1 and have more than 2 factors. For example, 4 has three factors 1, 2, and 4, thus a composite number. Again 6 has factors 1, 2, 3, and 6 and thus is also a composite number.

Some other examples include 8, 9, 10, 12, 14 and 16.

In contrast, numbers that are not composite are prime numbers. Such numbers only have two factors: 1 and the number itself. For example, 5 is divisible only by 1 and 5, and thus it is a prime number.

## Are 0 and 1 Composite Numbers?

Since 0 has infinite factors, it is not a composite number.

1 has only one factor, ‘1’ itself. So it is neither prime nor a composite number.

## List

Here we have listed down all the composite numbers from 1 to 100.

Thus, there are 74 composite numbers between 1 and 100.

## Chart

We can also represent the list of composite numbers in a chart, as it is visually more appealing and easy to use for various mathematical calculations. Here we have provided a chart from 1 to 100.

## How to Find Composite Numbers

As a composite number has more than two factors, we can determine if a given number is composite by finding its factors.

Factors of a composite number can be either prime or composite.

For example, 12 can be represented as 1 × 12 or 3 × 4 or 2 × 6

So 12 is a composite number with the factors 1, 2, 3, 4, 6, and 12. Here 4, 6, and 12 are composite numbers, while 2 and 3 are prime numbers.

Now rewriting 3 × 4 as 3 × 2 ×2 or 2 × 6 as 2 × 3 × 2, we get that each composite number can be represented as the product of two or more prime numbers.

Thus to find a composite number, we perform the divisibility test and check if it is completely divisible by at least one prime number smaller than itself.

For example, let us consider 40. As it is an even number, it is completely divisible by 2. It is also divisible by 5. Thus, it has more than two factors and is a composite number.

40 = 2 × 2 × 2 × 5 = 23 × 5

Similarly, 81 is a composite number as it is completely divisible by the prime number 3, and 81 = 3 × 3 × 3 × 3 = 34.

However, 41 is not divisible by any prime number like 2, 3, 5, 7, 11, 13, smaller than 41. Hence, it is not a composite number. It also cannot be represented as the product of two prime numbers as 41 = 1 × 41(where 41 is prime but 1 is not)

## Types

Composite numbers can be classified into two types:

### 1. Odd Composite Numbers

Odd composite numbers are all the odd natural numbers greater than 1, which are not prime.

Examples: 9, 15, 21, 27, 33

### 2. Even Composite Numbers

Even composite numbers are all the even natural numbers greater than 1, which are not prime.

Examples: All the even numbers except 2, such as 4, 6, 8, 12, 18, and 20 are a few examples.

## Smallest Composite Number

Looking at the set of natural numbers greater than 1, {2, 3, 4, 5, 6, 7, 8, 9,……}, we see that both 2 and 3 are prime numbers as both of them have exactly two factors (1, and the number itself).

Hence the smallest composite number is 4, which has more than two factors. It is also the smallest even composite number.

9 is the smallest odd composite number with 3 factors: 1, 3, and 9.

## Solved Examples

Which of the following is a composite number?
(a) 13
(b) 39
(c) 29
(d) 61

Solution:

(a) 13 has two factors: 1 and 13.
(b) 39 has four factors: 1, 3, 13, and 39.
(c) 29 has two factors only: 1 and 29.
(e) 61 has two factors: 1 and 61.
Hence option (b) is a composite number.

Identify whether the number is prime or composite
15, 27, 23, 49

Solution:

15 is divisible by 1, 3, 5, and 15.
27 is divisible by 1, 3, 9, and 27.
23 is divisible only by 1 and 23.
49 is divisible by 1, 7, and 49.
Thus 15, 27, and 49 are composite numbers, and 23 is a prime number.

Check if 51 is a composite number.

Solution:

51 is divisible by 3. So it has more than two factors.
Also, 51 = 1 × 51 = 3 × 17 is divisible by 1, 3, 17, and 51.
Hence, 51 is a composite number.

Is 121 a composite number?

Solution:

121 is divisible by 11 as 121 = 11 × 11.
Thus it has three factors: 1, 11, and 121.
So, it is a composite number.

Write the sum of the first four composite numbers.

Solution:

The first four composite numbers are 4, 6, 8, and 9.
Hence the sum is 4 + 6 + 8 + 9 = 27

Find if 364 is a composite number.

Solution:

As 364 is an even number, it is divisible by 2. So by the divisibility test, we can confirm that 364 is a composite number.

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 and 364 itself.