Composite numbers

  

Composite Numbers

In Mathematics, composite numbers are numbers that have more than two factors. These numbers are also called composites. Composite numbers are just the opposite of prime numbers which have only two factors, i.e. 1 and the number itself. All 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. In this article, we will learn the definition of composite numbers, properties, smallest composite number, even and odd composite numbers, list of composite numbers, and difference between prime and composite numbers along with many solved examples in detail.


Table of Contents:

Definition

Examples

Properties

List of composite numbers

How to find composite number

Types of Composite Number

Odd

Even

Smallest Composite Number

Difference Between Prime and Composite Numbers

Prime Factorisation of composite number

Solved Examples

Practice Questions

FAQs


What are Composite Numbers in Maths?

Definition 1: In Mathematics, composite numbers are numbers that have more than two factors.


Definition 2: The numbers which can be generated by multiplying the two smallest positive integers and contain at least one divisor other than the 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.


Is 0 a Composite Number?

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



Composite Numbers Examples

The examples of composite numbers are 6, 14, 25, 30, 52, etc, such that:


Composite numbers         Factors

6                                            1, 2, 3, 6

14.                                         1, 2, 7, 14

25.                                          1, 5, 25

30                                          1, 2, 3, 5, 6, 10, 15,                                                   30

52                                           1, 2, 4, 13, 26, 52

In all the above examples, we can see the composite numbers have more than two factors. There are a number of composite numbers we can list out of a set of natural numbers from 1 to 1000 or more. Let us see the list of composite numbers in the next section.



Properties of Composite Numbers

The properties of composite numbers are easy to remember.


Composite numbers have more than two factors

Composite numbers are evenly divisible by their factors

Each composite number is a factor of itself

The smallest composite number is 4

Each composite number will include at least two prime numbers as its factors (Eg. 10 = 2 x 5, where 2 and 5 are prime numbers)

Composite numbers are divisible by other composite numbers also


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 1 to 100


Composite Numbers Chart

Composite numbers chart


Download PDF – Composite Numbers

Composite Numbers 1 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.


How to Find 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.



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 on Composite numbers

Smallest Composite Number = 4

Smallest Prime Number = 2

Smallest Odd Composite Number = 9

Two-digit Smallest Composite Number = 10


Difference Between 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 Factorization of Composite Numbers

The list of composite numerals from 1 to 50 are given here with their prime factorization. You can see here how the composites are factorized 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 factorization.


Composite Numbers Prime Factorization

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

Comments

Post a Comment

Popular posts from this blog

BODMAS RULE IN MATHEMATICS

Image
  What is BODMAS ? The evaluation of an expression involving numbers is one of the basic tasks in arithmetic. If an expression contains addition (+), subtraction (-), multiplication (x), division (÷), bracket (), and Of (of), then the precedence of simplification of the operation is given by “BODMAS rule”. First, we have to know that what is  BODMAS rule ? Or What is BODMAS formula? BODMAS rule  is a rule or order that is used to simplify the arithmetic expression involving more operators in mathematics. When an equation involving more operators first we have to know that in which order we have to solve the expression. This problem is solved with the help of BODMAS rule. The full form of BODMAS is: B rackets (Parts of a calculation inside the bracket always come first). Precedence of brackets are : [{(bar)}] O rders (powers and square roots) D ivision M ultiplication A ddition S ubtraction Each letter of the word stands for the first letter of an operator. If an expressio...
Read more
Image
Pascal's Triangle Pascal’s Triangle  is a kind of number pattern.  Pascal’s Triangle is the triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression.  The numbers are so arranged that they reflect as a triangle. Firstly, 1 is placed at the top, and then we start putting the numbers in a triangular pattern. The numbers which we get in each step are the addition of the above two numbers. It is similar to the concept of  triangular numbers .  In this article, we are going to learn Pascal’s triangle history, definition, properties, patterns, formulas and examples with complete explanation. Table of contents: History Definition Construction How to use Patterns Properties Formula Expansion FAQs Pascal’s Triangle History Blaise Pascal was born at Clermont-Ferrand, in the Auvergne region of France on June 19, 1623. In 1653 he wrote the Treatise on the Arithmetical Triangle which today is known as the  Pascal’s Triang...
Read more

History of Statistics

 The early writings on statistical inference date back to Arab mathematicians and cryptographers, during the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains the first use of permutations and combinations, to list all possible Arabic words with and without vowels.[13] In his book, Manuscript on Deciphering Cryptographic Messages, Al-Kindi gave a detailed description of how to use frequency analysis to decipher encrypted messages. Al-Kindi also made the earliest known use of statistical inference, while he and later Arab cryptographers developed the early statistical methods for decoding encrypted messages. Ibn Adlan (1187–1268) later made an important contribution, on the use of sample size in frequency analysis.[13] The earliest European writing on statistics dates back to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.[14] Early applicati...
Read more