Composite Numbers

Dhristi JEE 2022-24

What are Composite Numbers?

In the subject of mathematics or math, composite numbers are defined as the type of numbers that have more than two factors. These numbers are different from prime numbers as prime numbers only have two factors. These factors are one and the number itself. Composite numbers are also simply known as composites.


Readers need to remember that all numbers that are not prime numbers can be categorized as being composite numbers. These numbers can also be divided by more than two numbers. For example, the number six is composite because it can be divided by 1, 2, 3, and 6.


Composite numbers can also be defined as the integers that can be generated by multiplying the two smallest positive integers. These numbers should also contain at least one divisor other than the number one. These numbers also have more than two composite factors. For example, any even number that is greater than 2 is a composite number.


Students are often asked to mention the difference between prime numbers and composite numbers. This is why it is advised that students should understand the concept of prime and composite numbers properly.


Also, another common question that students have on this topic is whether zero falls under the category of prime or composite numbers. The answer to this question is that zero does not fall under either of these categories of prime or composite numbers.


Keep in mind everything that we have discussed till now. Can you mention all the major composite numbers up to 200? If you can’t, then go through the section that is mentioned below.


4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 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, 198, and 200.


One should also look at lists mentioning composite numbers from 1 to 1000 to become more familiar with this topic.

 

How Can You Determine Composite Numbers?

Now, you must understand the meaning of consecutive composite numbers. You should also have a ready list prepared of all the composite numbers from 1 to 100. This is why it is now time to learn the process of finding out the values of composite numbers.


The process that you can follow to determine composite numbers is mentioned below.

  • Begin by finding out all the factors of a positive integer.

  • If a number only has two factors, which are one and the number itself, then classify it as a prime number.

  • If a number has more than two factors, then categorize it as a composite number.


For example, let’s assume that you have to find whether 14 is a prime or composite number. You must first begin with the understanding of what prime and composite numbers are. After that, you should find out the factors of 14.


We know that, 14 / 1 = 14


14 / 2 = 7


14 / 7 = 2


14 / 14 = 1


From this, it can be concluded that 14 is a composite number as it has more than one factor. Also, students should be familiar with all the composite numbers less than 20 without consulting a book.


The Different Types of Composite Numbers

In this section, we will look at the different types of composite numbers. According to experts, there are mainly two divisions of composite numbers. These divisions are:

  • Odd composite numbers or composite odd numbers

Odd composite numbers are all the composite numbers that are odd integers. For example, 9, 15, 21, 25, and 27.


  • Even composite numbers or composite even numbers

On the other hand, even composite numbers are all the composite numbers that are also even integers. For example, 4, 6, 8, and 10.


What are The Properties of Composite Numbers?

Composite numbers refer to the positive integers that are numbers that are formed by multiplying two smaller positive integers. The major properties of these composite numbers are that these numbers are evenly divisible by both smaller composite and prime numbers, that is, no special preference is given to the prime numbers or the composite numbers for becoming a factor of any number. The second property of composite numbers is that all composite numbers are made up of a combination of two or more prime numbers.


How are Composite Numbers Different From Prime Numbers?

The major difference between a prime number and composite number is that the prime numbers are only divisible by 1 and themselves, that is, such numbers have only two factors whereas composite numbers have more than two factors, that is, it is divisible by numbers other than 1 and itself also. Prime numbers can only be written in the form of a product of two numbers only while composite numbers can be written in the form of the product of more than two numbers. For example, 5 is a prime number as it has no factor other than 1 and 5 whereas 4 is a composite number because other than 1 and 4, 2 is also a factor of 4.


Learn About the Smallest Composite Number

Four is the smallest composite number. This is because, in the case of 4, there are more than two factors. The divisors of 4 are 1, 2, and 4. Also, you might want to note that the smallest prime number is 2, the smallest odd composite number is 9, and the two-digit smallest composite number is 12.


Prime Factorization of Commonly Used Composite Numbers

It is recommended that students should be familiar with composite numbers between 1 to 100 and their prime factorization. This is because students can be asked to answer questions related to that from the prime and composite number chapter. This is why we have created a list of prime factorization of composite numbers till 50. That list is mentioned below.


Composite Numbers

Prime Factorization

4

2 x 2

6

2 x 3

8

2 x 2 x 2

9

3 x 3

10

2 x 5

12

2 x 2 x 3

14

2 x 7

15

3 x 5

16

2 x 2 x 2 x 2

18

2 x 3 x 3

20

2 x 2 x 5

21

3 x 7

22

2 x 11

24

2 x 2 x 2 x 3

25

5 x 5

26

2 x 13

27

3 x 3 x 3

28

2 x 2 x 7

30

2 x 3 x 5

32

2 x 2 x 2 x 2 x 2

33

3 x 11

34

2 x 17

35

5 x 7

36

2 x 2 x 3 x 3

38

2 x 19

39

3 x 13

40

2 x 2 x 2 x 5

42

2 x 3 x 7

44

4 x 11

45

3 x 3 x 5

46

2 x 23

48

2 x 2 x 2 x 2 x 3

49

7 x 7

50

2 x 5 x 5


How to Recognize if a Number is Prime or Not?

The rules with which you can recognize if a number is prime or not. These rules are:

  • If a number is greater than 2 and is a multiple of 2, then, in that case, the number is not a prime number because it will have at least three factors, 1, 2 and the number itself.

  • If a number is greater than 3 and a multiple of 3 as well, then that number can also not be a prime number, because it has at least three factors 1, 3 and the number itself.

  • If a particular number is a multiple of 4, then it will also be a multiple of 2, therefore, such numbers can also not be considered as prime numbers.

  • If any number is greater than 5 and is also a multiple of 5, then it will not be a prime number. In other words, if a number ends with 0 or 5, then it will not be a prime number because in this case also, the number is divisible by at least 1, 5 and the number itself.

  • Similarly, if a number is a multiple of 6, then it will also be a multiple of 2 and 3, therefore such numbers can automatically rule out from the list of prime numbers as it will have at least five factors, that is, 1, 2, 3, 6 and the number itself.


Fun Facts About Composite Numbers

Did you know that prime numbers can only be divided by 1 and the number itself? On the other hand, composite numbers have more than two factors. Prime numbers can also be just written as products of two numbers. But composite numbers can be written as the products of more than two numbers. For example, 5 is a prime number, while 4 is a composite number.

FAQs on Composite Numbers

1. What is a Composite Number?

The numbers in math are broadly divided into two major categories, that is, prime numbers and composite numbers. A composite number is a positive integer or natural number that has more than one factor. For example, 15 is a composite number as it has multiple factors, including 1, 3, 5, and 15. Composite numbers are numbers that have more than two factors, that is, numbers other than 1 and itself. In other words, a composite number is one that is divisible by numbers other than 1 and itself.

2. Is 2 a Composite Number?

2 is not a composite number because it has only two factors. Since 2 is divisible by only 1 and itself, therefore, it cannot be considered as a composite number because the criteria for a number to be called composite is that it should have more than 2 factors, that is, 1 and the number itself. Thus, 2 is a prime number, according to which a number is said to be prime if it has only 2 factors, that is, 1 and the number itself, for example, 2.

3. Is 9 a Composite Number?

Yes, 9 is a composite number as it has more than two factors, including 1, 3, and 9. For a number to be considered as a composite, it should have more than two numbers as its factor, and since 9 has 3 factors, therefore, it will be considered as a composite factor. If the number would have only two numbers as its factors, that is 1 and the number itself, then, in that case, the number would have been a prime number and not a composite number.

4. Is 19 a Prime or Composite Number?

19 is a prime number as it has only two factors. Prime numbers are the ones that have only two factors, one is the number 1 and the other is the number itself. Since 19 is divisive by only 1 and 19 therefore, it is a prime number. If the number would have had more than 2 factors, then that number would have been considered as a composite number instead of it being considered as a prime number.

5. Find Out the Total Number of Composite Numbers Between 1 and 10.

Composite numbers refer to those numbers which have more than two factors, that is, these numbers are also divisible by numbers other than 1 and the number itself. There are five composite numbers between 1 and 10. These numbers are 4, 6, 8, 9, and 10. Therefore, between 1 and 10, there are only 5 numbers which are divisible by other numbers as well, except for 1 and the number itself. The remaining five numbers between 1 and 10 are prime numbers, that is they are divisible by only two numbers, which are 1 and the number itself.

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