Natural Numbers and Whole Numbers

In Mathematics, Number system consists of all types of numbers which is used to perform various calculations. The types of numbers are natural numbers and whole numbers, prime numbers and composite numbers, integers, real numbers and imaginary numbers.

Natural numbers and whole numbers, we have studied since our primary classes. Basically, natural numbers are set of positive integers whereas natural numbers along with zero(0) are called as whole numbers, where zero is an undefined identity which produces a null result. Zero is the basic difference between natural and whole numbers.

Natural and whole numbers in Maths have equal importance. Suppose, if we have to count for a number of objects, then we start from number 1,2,3,4 and so on but once these objects are all vanished then what count does it gives is zero. There is a further classification of natural numbers.

Natural Numbers

Natural numbers are the set of positive integers, from 1 to ∞ but it doesn’t include fractional and decimal numbers. They are also known as counting numbers.

Natural Numbers: 1,2,3,4,5,6,…….,∞

Types of natural numbers:

  • Prime Numbers
  • Even and Odd numbers
  • Composite numbers
  • Co-prime numbers
  • Perfect numbers

Whole Numbers

Whole numbers are also a set of positive integers starting from 0 to ∞. They also don’t include fractional and decimal part.

Whole Numbers: 0,1,2,3,4,5,6,…….,∞

Natural Numbers and Whole Numbers Properties

    • Addition Property

When two natural numbers are added, it results in natural number only.

Eg: 34+45 = 79

When two whole numbers are added, it results in the whole number only.

Eg: 6+0= 6

    • Subtraction Property

When two natural numbers are subtracted it may or may not result in a natural number.

Eg: 5 – 2 = 3 is natural number

But 2 – 5 = -3 is not a natural number

Same is the condition for whole numbers. If two whole numbers are subtracted, then its not necessary it will result in the whole number.

    • Multiplication Property

When two natural numbers or whole numbers are multiplied, then it always results in natural numbers and whole numbers respectively.

Eg: 2 X 6 = 12 is a natural number

4 X 0 = is a whole number, where 4 and 0 are also whole numbers.

    • Division Property

Division of two natural numbers and whole numbers may or may not result in natural and whole numbers respectively. It means if the result is in fraction or decimal, then they are not considered as natural and whole numbers.

Eg: 4/2 = 2 is natural as well as the whole number

But 5/2 = 2.5 is neither natural nor whole number.