in Definitions

Types of Numbers in Mathematics

Hi, today am going to discuss about types of numbers in mathematics. In general we have so many types of numbers are there in maths. In our daily life these types of numbers plays an important role. So let’s see what are the different types of numbers and its definitions with some example.

types of numbers in mathematics

Types of Numbers:

Natural Numbers:

Counting numbers are called Natural Numbers.

It is denoted by ‘N’.

The set of Natural Numbers are represented by N= {1, 2, 3———}

Smallest number in Natural Number is 1.

Largest Number in Natural Number is can’t be defined.

Successor:

For any given Natural Number, add one to that number is called Successor.

Eg: successor of 5 is 5+1=6.

Predecessor:

In any given Natural number, subtract one to that number is called predecessor.

Eg: predecessor of 8 is 8-1=7

Whole Numbers:

Natural Numbers including zero is called whole numbers. It is denoted by ‘W’.

The set of Whole Numbers are represented by W= {0, 1, 2……..}

Smallest number in Whole Number is 0.

Largest Number in Whole Number is can’t be defined.

  • All Natural numbers are Whole numbers but not all whole numbers are Natural numbers.

Even Numbers:

The Natural Numbers which are exactly divisible by 2 are called even numbers.

The set of even numbers are denoted by ‘E’.

E= {2, 4, 6, 8…………..}

types of numbers in mathematics

 

Odd Numbers:

The Natural Numbers which are not exactly divisible by 2, leaves remainder 1 are called as odd numbers.

The set of odd numbers are denoted by ‘O’.

O= {1, 3, 5, 7…………..}

Properties of Even and Odd numbers:

  • The sum of any two even numbers is an even number.

Eg: 2+4=6

18+20=38

  • The difference of any two consecutive even numbers is an even number.

Eg: 20-18=2

14-6=8

  • The product of any two even numbers is an even number.

Eg: 24=8

64=24

  • The sum of any two odd numbers is an even number.

Eg: 3+3=6

20+20=40

  • The difference of any two consecutive odd numbers is an even number.i.e, 2

Eg: 9-7=2

19-17=2

  • The product of any two odd numbers is an odd number.

Eg: 57=35

117=77

  • The sum of one even and one odd number is always an odd number.

Eg: 11+12=23

  • The product of one even number and one odd number is an even number.

Eg: 34=12

 

  • General form of an odd number = 2n-1
  • General form of an even number=2n

 

Types of numbers based on number of factors:

Prime Numbers:

A prime number has only two factors one and itself. It is greater than ‘1’.

Eg: 2, 3, 5, 7…………

Composite Numbers:

A Natural number having at least three factors.

  • 1 is neither prime nor prime

Eg: 4 is a composite number?

Factors of 4= 1, 2, 4

Yes 4 is a composite number it has three factors.

types of numbers

Multiple:

The product of a number and counting numbers are known as multiples of that number.

Eg: multiples of 4 are 4, 8, 12, 16………….

  • Every multiple of a number is greater than or equal to that number.
  • The number of multiples of a given number is infinite.

 

Factor:

If a number ‘x’ divides another ‘y’ exactly then that x is a factor of y.

  • Every factor of that number is less than or equal to that number.
  • Number of factors of a given number is finite.

Eg: 6 divide 18 exactly

Then 6 is a factor of 18.

types of numbers

 

Prime factor:

If a factor of a given number is prime, then the factor is called a prime factor.

Eg: factors of 30 are 1, 2,3,5,6,10,15,30.

Out of these prime factors are 2, 3, and 5

Twin Primes:

The difference of pair of prime numbers is 2.

Eg: (11, 13), (17, 19)

Perfect number:

A number in which sum of all its factors is equal to twice the number is called a perfect number.

Eg: 28 is a perfect number or not?

Factors of 28 =1, 2,4,7,14,28

Sum of factors = 1=2+4+7+14+28=56 =2(28)

So, 28 is perfect number.

Amicable numbers:

Two numbers are said to be amicable numbers, if the sum of the divisors of one number excluding itself is equal to the other number.

Eg: 220 and 284 are amicable numbers

Sum of divisors of 220 (except 220) = 1+2+4+5+10+11+20+22+44+55+110=284

Sum of the divisors of 284(except 284) = 1+2+4+5+71+142=220

 

Relatively prime numbers:

Two positive integers ‘a’ and’b’ are said to be relatively prime or co- primes, If they do not have any common factor other than one.

Eg: 25 and 81 are co-primes.

 

I hope you liked the post on types of numbers. In future I will update the classification of numbers according to its nature and its importance.

 

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Hi am a blogger so am interested to write more on Technology and Mathematics