## Composite Numbers

**Composite Numbers: **In Mathematics, a number is classified into various categories like Prime numbers, Whole numbers, Complex numbers, Rational numbers, and so on. A composite number is also one of the classifications of the number. You have come across 0,1,2,3,4,5,6,7,8,9,…… when you started learning countings and tables. These numbers can be classified on the basis of the number of factors that they have. If a number has only two factors – 1 and the number itself, then it is a prime number. When a number is made by multiplying more than two numbers, then it is a composite number. These multiples are also known as factors. In another way, composite numbers are just the opposite of prime numbers. In this article, you will learn about composite numbers, their factors, properties, and various facts about composite numbers.

## Composite Number Definition

**Composite numbers are defined as numbers that have more than two factors**. Composite numbers can also be defined as a number that is divisible by more than two numbers or a number that is divisible by at least one number other than 1 and the number itself.

Composite Number Definition:A natural number or a positive integer which has more than two factors is called acomposite number.

For example, **8 has multiples like 1 x 2 x 4 x8**and 10 has multiples like 1 x 2 x 5 x 10. So, 8 and 10 are composite numbers as they are divisible by more than two numbers. Here are some more examples that help you in better understand the concepts of composite numbers 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. In between 1 to 50 you will find that the maximum numbers are composite. So, all the natural numbers which are not prime numbers are composite numbers as they can be divided by more than two numbers.

To find whether the given number is a composite number, we simply do a divisibility test that helps us to determine whether a number is a prime or a composite number. This Divisibility test means that a number is divided completely without any remainder, by another number.

## Properties of Composite Numbers

A number must have the following properties to be called a composite number, let’s have a look at what those properties are:

- Composite numbers are evenly divisible by smaller numbers that can be prime or composite.
- Composite numbers have more than two factors.
- Each composite number is a factor of its magnitude.
- Composite numbers are divisible by other composite numbers
- Each composite number has at least two prime numbers as factors.

If we take 42 as an example to understand the properties of composite numbers.

42 = 1 x 2 x 3 x 6 x 7 x 14 x 21 x 42

The prime factorization of 42 is 2 x 3 x 7, so here 42 has three prime numbers as a factor and is evenly divisible by eight numbers.

## Composite Numbers 1 to 100

There are **a total of 74 composite numbers between 1 and 100**.The list of all composite numbers between 1 to 100 is given below.

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 | 77 | 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 |

## Types of Composite Numbers

To understand the types of composite numbers, you must be aware of even and odd numbers. So, A number that is completely divided by two without leaving any remainder is known as an even number and those numbers which are not completely divisible by two are known as odd numbers. There are two types of composite numbers

- Even Composite Numbers
- Odd Composite Numbers

### Even Composite Numbers

The composite number which is also an even number is known as an **even composite number**. So, All the even numbers which are not prime are even composite numbers. **4 is the smallest even composite number.**

For Examples: 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. Again if we consider all the numbers between 1 to 30, we will find all these numbers as even composite numbers. You can check whether they are completely divisible by two or not. You will find that they are even numbers and hence we called them even composite numbers.

### Odd Composite Numbers

A composite number that is an odd number is known as an **odd composite number**. We can also define it as all those odd integers which are not prime are odd composite numbers. **9 is the smallest odd composite number.**

For Examples: 9, 15, 21, 25, 27. These are the composite numbers that are not divisible by two. So, If we consider all the numbers between 1 to 30, these five numbers are odd composite numbers. Can you discover more odd composite numbers by yourself?

## Smallest Composite Number

Can you guess which is the smallest composite number and why? The answer is very simple, 4 is the smallest composite number. If you have a look at these numbers like 1, 2, 3, 4, and 5, you will find that 1 is neither a prime number nor a composite number, as 1 can only be divided by one the number, 1 itself, so by the definition of the composite numbers, it does not fulfill the criteria of composite numbers. Now we have the next number 2, which is a prime number as it has only two factors which are 1 and itself. Again 3, which is also a prime number having only two factors. Now, we got 4, which is the first number having more than two factors which are 1, 2, and 4, that’s why we consider 4 as the smallest composite number. After 4, 6 is the next composite number as again 5 is a prime number which has only two factors 1 and 5 itself.

### Points to remember in Composite Number:

- All even numbers other 2 are composite numbers.
- 4 is the smallest composite number.
- 10 is the smallest two-digit composite number.
- 9 is the smallest odd composite number.
- 100 is the smallest and 999 is the largest three-digit composite number.
- Each composite number can be written as a product of two or more prime numbers.

## Solved Examples of Composite Numbers

**Q1. What is the prime factorization of 55?**

Ans: The prime factorization of 55 is **5 and 11.**

**Q2. Is 211 a composite number? Explain.**

Ans: **No, 211 is not a composite number**because 211 doesn’t have more than 2 factors. The number 211 has only two factors, i.e. 1 and 211.

**Q3. Find out which one of the following is not a composite number.**

15, 35, 53, 77, 93

Ans: The correct answer is **53. **53 is not a composite number as It is only divisible by 1 and itself.

**Q4. Find the product of the first 4 composite numbers.**

Ans: The first four composite numbers are 4, 6, 8, and 9. Now we have to multiply these composite numbers to get the product.

So, 4x 6x 8x 9 = 1728.

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