Composite numbers is one of the types of numbers. They hold an important place in various mathematical concepts. We all know that the numbers can be classified as odd and even numbers, rational and irrational numbers, prime and composite numbers and so on. This page will make you understand about composite numbers in detail. First a brief description of the concept is given and later moving on to explanation of problems.

First, let’s know what is a composite number? A number which is not a prime number is known as a composite number. Actually a composite number is opposite to prime numbers. More elaborately, a positive integer that has at least one number which divides the given integer other than one and itself.

According to a more formal definition –

If x is a composite number, then there must exist two positive integers p and q, such that x = p * q ; provided that p and q are not equal to 1 and x.

For example –

6 = 2 * 3, 10 = 2 * 5

Every positive number has to be either prime or composite. The numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, … are included in the list of prime numbers.

## Composite Number Definition

A number which is dividing by positive divisor other than one or itself is called as composite number. A composite number is always positive integer. In other words, If the integer n is greater than zero and the divisors are 1 < a, b < n means the integer ‘n’ is composite number.

### Is 1 a Composite Number?

No, 1 is not a composite number. Composite numbers is the one that is evenly divisible by a some number other than itself or the number 1.

### What is a Composite Number?

What are composite numbers? Composite numbers are the numbers which have more than two factors and also is not a prime number, then the number is called composite number. We all know that natural numbers includes the set containing numbers starting from 1 to infinity. I.e.

N = {1, 2, 3, 4 … infinity}

If a given number is divided by a Natural number without leaving any remainder then that natural number is called a factor. This is also called Divisor. Observe the following table, in which factors of some numbers are given. For example 1, 2 and 4 divide 4 without leaving any remainder. So 1, 2 and 4 are factors of the given number 4.

Numbers | Factors | Number of Factors |

1 | 1 | 1 |

2 | 1, 2 | 2 |

3 | 1, 3 | 2 |

4 | 1, 2, 4 | 3 |

5 | 1, 5 | 2 |

6 | 1, 2, 3, 6 | 4 |

7 | 1, 7 | 2 |

8 | 1, 2, 4, 8 | 4 |

9 | 1, 3, 9 | 3 |

10 | 1, 2, 5, 10 | 4 |

11 | 1, 11 | 2 |

12 | 1, 2, 3, 4, 6, 12 | 6 |

There are numbers, having exactly two factors 1 and the number itself. 2, 3, 5, 7 and 11 have two factors only. They are one and the number itself. These are called Prime numbers. A number which has two factors,1 and the number itself is called a prime Number.

## Composite Numbers from 1 to 100

A total of 74 composite numbers are there between 1 to 100. Below you can see the list of composite numbers from 1 to 100:

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.

## How to find Composite Number

Following are the steps to find the composite number.

- Step 1: We know that 2 are a prime number. So Encircle 2 crosses out all the multiples of 2, other than 2 itself, i.e. 4, 6, 8 and so on.
- Step 2: See the next prime number 3 and cross out all multiples of three except 3.
- Step 3: See the next prime number 5 and cross out all multiples of three except 5.
- Step 4: This process is continued. see the numbers are circled or crossed out.

All the crossed out numbers, other than 1 are composite numbers. All the encircled numbers are prime numbers.

## Examples of Composite Numbers

**Question 1: Check whether 121 is composite number**

Solution:

First we have a to find the factor for 121

The factor of 121 is =1, 11,121

So it has more than two factors.

Correct answer is 121 is composite number

**Question 2: Check if 101 is composite number.**

Solution:

The factor of 101 is =1,101

It has only two factors

Correct answer is 101 is not a composite number

**Question 3: Check 212 is composite number or not?**

Solution:

The factor of 212 is = 1, 2, 4, 53, 106, 212.

It has more than two factors

Correct answer is 212 is composite number.

### Summary

From the above discussion, following rules can be drawn.

- 1 is neither a prime nor a composite number.
- 2 is the first prime number.
- Any even number greater than 2 is not a prime number.
- Any prime number greater than 2 is an odd number.
- 2 is an even number and also a prime number.
- If there exists a composite number in between two prime numbers then such a pair of prime numbers is called twin primes.
- For Example: 3 & 5, 5 & 7, 11 & 13, 17 & 19, 41 & 43 are the list of Twin primes in the range of 1 to 100.

## Composite Number Calculator

Is it composite or prime number? – Find out if it is a composite number or prime number using calculator below.

### Composite Number Calculator

**Steps to use composite number calculator:**

- Enter the number in the input field
- Next, click on the calculate button.
- Now, it will display the given number is a composite or prime.

That’s it!

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