Composite Numbers

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:

  • 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.

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.

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.

Updated: July 14, 2021 — 1:06 am

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