Composite Numbers : Definition, Types, and Lists

In mathematics there is a lot of fun with playing numbers. As we know all these sets of numbers then only we will play with them. Let start with composite number. To know about composite numbers first we have to know about prime numbers also.

We know that the set of natural numbers N = {1, 2, 3, 4, 5,…} is classified into set of prime numbers and set of composite numbers. And both these sets of numbers are contradictory to each other.

composite numbers

Composite numbers:

Mathematics is always fun and exciting where we get numerous chances to play with numbers. Even we can solve many critical problems just by applying tricks of numbers. Before that we must learn all the sets of numbers and various formulae to apply those at correct place. There are commonly known two sets of numbers which are prime number and composite number in n set of numbers starting like 1,2,3,4,5,6,7,8,9,10…. To know details about composite number we have to know about prime number properly. Prime numbers are those which have only two factors 1 and the number itself. Both prime numbers and composite numbers are contradictory to each other. 1 is the number which is neither prime number nor composite number. 2 is the smallest prime number and other prime numbers are 3, 5, 7,11,13,17…and so on. On the other hand, composite numbers are those which have more factors except 1 and the number itself. Two is the only even prime number where all other prime numbers are odd.

Composite numbers have always more than two factors where 2 is the common factor. 4 is the smallest composite number where factors are 1,2,4. Other composite numbers are 6,8,10,12,14,16,18,20,22,24,26,28,30 and so on. 1 and 0 are numbers which are neither prime nor composite number. Every natural number is divisible by 1 and the number itself irrespective of being prime number or composite number. From 1 to 100 there are total 25 prime numbers and 75 composite numbers. All the even numbers which are not prime are composite numbers where we can find 2. Composite number is a positive integer like all other natural numbers. After knowing about the factors we can easily find prime factors from prime numbers. Composite number can be formed by multiplying two smaller positive integers. Properties of one composite number can be found from its factors. There are various types of composite number like even, odd etc. which students will understand after dividing its factors easily.

Prime numbers are the numbers which are having only two factors i.e. 1 and the number itself.
And the prime numbers starts from 2, 3, 5, 7, 11, 13, 17…
While the composite numbers are the numbers which are having the factors more than 1 and the number itself.
Let us suppose XY be the natural number, then XY is prime number only when it has factors 1 and the number XY itself.

Hence, we write as

For example:

2 is the lowest and first prime number.
2 is the only one even prime number, it is having factors 1 and the number 2 itself only.

3 is also prime number as its factors are only 1 and 3.
Similarly, 5, 7, 11 are also the prime number because they are having the factors only 1 and the number itself.

Hence, we write for prime numbers as

Now, the numbers which are not prime numbers are the composite numbers. Composite numbers are the numbers which are having the factors other than 1 and the number itself.
The composite numbers starts from 4, 6, 8, 9…
Let us suppose XY is the composite number then it is having factors 1, XY and other factor suppose x also.

Hence, we write as,

For example:

4 is the first composite number because its factors are 1, 2, and 4.

Hence, 4 = 1*4 = 2*2

6 is also the composite number because its factors are 1, 2, 3, and 6.

Hence, 6 = 1*6 =2*3

8 is also the composite number because its factors are 1, 2, 4, and 8.

Hence, 8 = 1*8 = 2*4

9 is also the composite number as its factors are 1, 3, and 9.

Hence, 9 = 1*9 = 3*3

NOTE:

1 and 0 are neither prime nor composite numbers.
And every natural number is divisible by 1 and the number itself.

Composite numbers between 1 and 100:

The number which are not prime numbers are the composite numbers.

The composite numbers between 1 and 100 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, 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.

Thus, there are total 74 composite numbers between 1 and 100, because 25 are the prime numbers between 1 and 100. And 1 is neither prime nor composite number.

Also See: Is 2000 a Composite Numbers

Smallest composite number:

The smallest and first composite number is 4. And 4 is the even composite number also.

We know that, 2 is the only one even prime number and all the other remaining prime numbers are odd prime numbers only.

But in case of composite numbers, there even and odd composite numbers are also present. We see in detail about even and odd composite numbers.

Even composite numbers:

All the even numbers which are not the prime numbers are the even composite numbers.
That means they are having the common factor as 2.

For example:

4, 6, 8, 10, 12, 14, 16…. Are the some even composite numbers.

Odd composite numbers:

All the odd numbers which are not prime numbers are the odd composite numbers.
And these numbers are having odd numbers as factors also.

For example:

9, 15, 21, 25, 27,… are the odd composite numbers.

Fun fact:

The numbers except 0, 1 and 2, which are having unit digit as 0, 2, 4, 6 and 8 are the composite numbers always, we can say them directly that they are composite numbers only.

For example:

If we see the table of 11 which is 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20.
Then the numbers having unit digits 0, 2, 4, 6 and 8 are 12, 14, 16, 18 and 20 are the composite numbers directly, because they are having the common factor as 2 other than 1 and the number itself.
And the remaining numbers 11, 13, 15, 17, and 19 we have to check they are prime or composite.
In this way, we can easily predict the numbers are prime or composite.

Important Links:

Number Names MCQ

Number System MCQ

Ordinal Numbers MCQ

Consecutive Numbers MCQ