### What are Whole Numbers ?

Whole numbers are the set of positive integers. They do not have any decimal or fractional part. Natural numbers along with zero(0) are whole numbers.*Closure Property Of Whole Numbers*

• Addition of whole numbers always gives a whole number. Thus whole numbers are closed under addition.

Eg. 5+7 = 12

• Subtraction of whole numbers does not always give a whole number. Thus whole numbers are not closed under subtraction.

Eg. 5-7 = -2, which is a negative integer and not a whole number.

• Multiplication of whole numbers always gives a whole number. Thus whole numbers are closed under multiplication.

Eg. 5x7 = 35

• Dividing a whole number by another does not always give a whole number. Thus whole numbers are not closed under division.

Eg. 5÷7 = a fraction, thus it will not be a whole number.

Natural and Whole numbers on number line |

### What are Natural Numbers?

Natural numbers are the set of positive integers, that is, integers from 1 to ∞ excluding fractional n decimal part. They are whole numbers excluding zero. Natural Numbers are also called counting numbers.Natural Numbers can further be sub-divided into different types :-

1)

*Even and odd Numbers*

2)

*Prime Numbers*

3)

*Relatively prime/ co-prime numbers*

4)

*Composite numbers*

5)

*Perfect numbers*

**What is Zero ?**

Zero is the only whole number which is not a natural number. It is represented by 0. "Zero is the only difference between natural and whole numbers."

*Properties of ZERO - 0*

• Zero added to any number gives the number itself. Hence, 0 is the additive identity for all numbers.

• Multiplication with zero- 0 multiplied with any number always gives 0.

• Zero divided my any number(except 0) gives 0.

• Any number divided by 0 is not defined.

• Zero raised to any power(except 0) gives 0.

• Zero to the power 0 (0

^{0}) is not defined.

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