Composite Numbers

Definition of composite numbers: Composite numbers are the numbers which have factors other than 1 and the number itself. It is also mentioned as composites. In Number System, the integers can be classified into two types namely, positive integers and negative numbers. These integers can be further classified into many types such as even and odd numbers, prime and co-prime numbers, composites, etc. Composites are the just opposite form of prime numbers. The smallest prime number is 2, which has factors 1 and itself. In this article, let we will learn the definition of composite numerals, the difference between composite and prime numbers, about the smallest composite number along with its types, examples and list of composites from 1 to 100.

What are Composite Numbers?

The integers which can be generated by multiplying the two smallest positive integers and contains at least one divisor other than number ‘1’ and itself is known as composite numerals or numbers. It is neither a prime number nor a unit. We can also say, any number which is not a prime number is a composite and has more than two factors. This is the general difference between composite and prime numbers. Let us learn now how to figure them out.

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.

Consider the example, 10 is a composite number. Because it is the product of the two smallest positive integers 2 × 5 and has factors 1, 2 and 5. Let us discuss more briefly here.

Types of Composite Numbers?

There are two main types of composite numbers 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.

Consider the numbers 1, 2, 3, 4, 9, 10, 11,12, and 15 . Here 9 and 15 are the odd composites because those two numbers have the odd divisors and satisfy the composite condition.

Even Composite Numbers

All the even integers which are not prime are even composite numbers. Examples of composite odd numbers are 4, 6, 8, 10, 12, 14, 16, etc.

Consider the numbers 1, 2, 3, 4, 9, 10, 11,12, and 15 again . Here 4, 10 and 12 are the even composites because those two numbers have the odd divisors and satisfy the composite condition.

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 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).

Composite Numbers List From 1 to 100

Here is the list of composite numerals from 1 to 100 for students. They 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.

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

Difference between Prime and Composite Numbers

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 Factorisation of Composite Numbers

The list of composite numerals from 1 to 50 are given here with their prime factorisation. You can see here how the composites are factorised in prime numbers. Check the below table to understand better. With the help of this table, you can also find the composites beyond 50 with their prime factorisation.

Composite Numbers Prime Factorisation
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 4 × 11
45 3 × 3 × 5
46 2 × 23
48 2 × 2 × 2 × 2 × 3
49 7 × 7
50 2 × 5 × 5

To learn more about the different types of numbers, download BYJU’S -The Learning App from the Google play store and watch interactive videos.

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