Natural Numbers and Whole Numbers

The counting numbers that begin from 1 are natural numbers whereas natural numbers along with zero(0) are called whole numbers. Zero is the primary dissimilarity of natural and whole numbers. Both natural and whole numbers have no fractional or decimal parts. 1 is the smallest natural number while 0 is the smallest whole number. Let's discuss the difference and similarities between natural numbers and whole numbers in this article.

Natural Numbers
The set of positive integers, from 1 to ∞ and doesn’t include fractional and decimal numbers are known as natural numbers. Natural numbers are also called counting numbers (Natural Numbers: 1, 2, 3, 4, 5, 6,…….,∞).
Natural numbers are the numbers useful for counting physical objects. They start with 1 and go till infinitely. Natural numbers are denoted by the symbol N. Natural numbers act as a subset of the real numbers. Therefore, we can say that every natural number is a real number. For example, 32, 45, 1, 28 are all natural numbers.

Whole Numbers
The set of positive integers including 0, that is from 0 to ∞ which does not include fractional and decimal numbers are known as whole numbers (Whole Numbers: 0, 1, 2, 3, 4, 5, 6,…….,∞). Basically, all of the natural numbers and the number zero are whole numbers. 0 is the smallest whole number. Positive integers and natural numbers are also whole numbers. For example  0, 85, 57,  27 are all whole numbers.

Look at the image given below to understand the natural numbers and whole numbers. 

The following points listed below show the difference between natural numbers and whole numbers.

• Zero is not a part of natural numbers and the counting numbers starts from 1 (1, 2, 3, 4, etc), whereas zero is a part of whole numbers and the series of whole numbers begin with zero (0, 1, 2, 3, 4, etc).
• 1 is the smallest natural number whereas 0 is the smallest whole number.
• The letter “N” is the symbol for natural numbers and the letter “W” is for whole numbers.
• All the natural numbers are whole numbers but all the whole numbers are not natural numbers as zero is not included in natural numbers.

The following points listed below show the similarities between natural numbers and whole numbers.

• Decimal numbers, fractional numbers, negative integers are not included in whole numbers and natural numbers.
• All-natural numbers are whole numbers.

Given below are the fundamental operations along with examples. 

• Addition: When two natural numbers or whole numbers are added, it gives results in a natural number or whole number. For example: 75 + 25 = 100
• Subtraction: When two natural numbers or whole numbers are subtracted it may or may not result in a natural number or whole numbers. For example: 8 - 2 = 6 is natural or whole number, But 2 – 8 = -6 is not a natural or whole number.
• Multiplication: When two natural numbers or whole numbers are multiplied, then it gives results in natural numbers or whole numbers. For example, 6 × 7 = 42 is a natural number or whole number. Note if 0 is multiplied by any number it will give a result in a whole number, not in a natural number. For example, 0 × 5 = 0 which is a whole number, not a natural number.
• Division: If we divide two natural numbers or whole numbers (other than 0) they may or may not result in natural and whole numbers. Sometimes results can come in fractions or decimals and they're not part of whole numbers and natural numbers. For example, 8/2 = 4 is a natural number, But 9/2 = 4.5 is not a natural or a whole number. Note if 0 is divided by any number it will give the result in the whole number, not in the natural number. For example, 0 ÷ 5 = 0 which is a whole number, not a natural number. Also, when we divide any number by 0, the value is always not defined.

Natural Numbers and Whole Numbers Related Articles

Check out the important topics mentioned below to learn more about natural numbers and whole numbers.

• Whole Numbers
• Natural Numbers 
• Integers
• Fractions
• Decimals 
• Composite Numbers

Are Natural Numbers Always Whole?

The whole numbers include all the natural numbers and zero, therefore all natural numbers are whole numbers, but as zero is not a part of natural numbers so all whole numbers are not natural numbers.

Is 7 a Whole Number or Natural Number?

7 is a whole number as well as a natural number because it is a part of a set of whole numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, etc) and natural numbers (1, 2, 3, 4, 5, 6, 7, 8, etc).

What is the Largest Natural Number?

The next natural number can be found by simply adding 1 to the current number and it can continue till infinite, so we cannot say that there is a particular number that is the largest natural number.

What are the Types of Natural Numbers?

The following are the types of natural numbers:

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

Is 8.1 a Whole Number or Natural Number?

8.1 is neither a natural number nor a whole number because the number is in decimal and we know that both natural numbers and whole numbers do not have any decimal parts.

What are the Similarities Between Natural Numbers and Whole Numbers?

Natural numbers and whole numbers do not include fractional and decimal parts and negative integers such as 8/9, 4.5, or -56. This is one of the similarities between natural numbers and whole numbers.

What is the Difference Between the Sets of Whole Numbers and Natural Numbers?

The difference between whole numbers and natural numbers set is that the set of whole numbers contains zero and the set of natural numbers does not contain zero.