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Here you will learn about natural numbers, including the types of natural numbers and properties of natural numbers.
Students will first learn about natural numbers in Kindergarten with counting and cardinality and extend that knowledge through elementary school into middle school with properties of addition and multiplication.
Natural numbers help you count and represent objects or quantities. They are also called “counting numbers”. The set of natural numbers, usually represented by N, can be defined as positive whole numbers beginning with 1.
N = \{1, 2, 3, …\}This number line shows the first 7 natural numbers.
Let’s look at some types of natural numbers and properties of natural numbers.
Prime and Composite Natural Numbers \hspace{1cm}
A prime number is a number with exactly 2 has two factors: \hspace{1cm}
7 has two factors:
 A composite number is a number with more 4 has three factors: \hspace{1cm}
12 has six factors:

Stepbystep guide: Prime number
Even and Odd Natural Numbers \hspace{1cm}
Even numbers are divisible by 2 without Every other number on the number line 
Odd numbers are not divisible by 2 without Every other number on the number line 
\bf{1} . Closure Property of Natural Numbers 

The sum and product of two natural numbers are also natural numbers.
The closure property does not work all the time for subtraction and division.

\bf{2} . Associative Property of Natural Numbers 

The sum and product of three natural numbers are the same even if the numbers (1 + 3) + 5 = 9
(1 \times 3) \times 5 = 15
The associative property does not work all the time for subtraction and division.

Step by step guide: Associative Property
\bf{3} . Commutative Property of Natural Numbers 

The sum and product of two natural numbers is the same even if the order is
The commutative property does not work all the time for subtraction and division.

Stepbystep guide: Commutative Property
\bf{4} . Distributive Property of Natural Numbers 

For three natural numbers, multiplication is distributive over addition and subtraction 
Stepbystep guide: Distributive Property
How does this apply to kindergarten through 6th grade?
In order to classify natural numbers:
In order to apply a property of natural numbers:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!
DOWNLOAD FREEIs the number identified on the number line a natural number?
Natural numbers are whole positive numbers beginning with 1.
2Show whether the number fits or does not fit the definition.
The number identified on the number line is \, \cfrac{2}{5} \, which is a fraction.
So, the number identified on the number line is not a natural number.
Is 13 an odd natural number?
Recall the definition of the type of number needed.
An odd number is not divisible by 2 without a remainder. Odd numbers end in 1, 3, 5, 7, 9.
Show whether the number fits or does not fit the definition.
13 is not divisible by 2 without a remainder and ends in a 3.
So, 13 is an odd number.
Is 19 a prime number?
Recall the definition of the type of number needed.
A prime number is a number with exactly two factors: itself and 1.
Show whether the number fits or does not fit the definition.
The factors of 19 are 1 and 19.
So, 19 is a prime number.
Find the missing number using the associative property of addition.
(5 + 2) + \, \rule{0.5cm}{0.15mm} \, = 5 + (2 + 9)
Recall the property.
The associative property of addition is (a + b) + c = a + (b + c)
Use the property to get an answer.
(5 + 2) + {\color{blue} 9} = 5 + (2 + 9)
9 is the missing number because (5 + 2) + 9 = 5 + (2 + 9) = 16
Find the missing number using the commutative property of multiplication.
19 \times 12 = 12 \times \, \rule{0.5cm}{0.15mm}
Recall the property.
The commutative property of multiplication is a \times b = b \times c
Use the property to get an answer.
19 \times 12 = 12 \times {\color{blue} 19}
19 is the missing number because 19 \times 12 = 228 and 12 \times 19 = 228
Find the missing number in the distributive property equation.
8 \times (5 + 3) = \, \rule{0.5cm}{0.15mm} \, + 24
Recall the property.
The distributive property is a \, (b + c) = ab + ac
Use the property to get an answer.
8 \times (5 + 3) = {\color{blue} 40} + 24
\color{blue} 40 is the missing number.
This natural numbers topic guide is part of our series on types of numbers. You may find it helpful to start with the main types of numbers topic guide for a summary of what to expect or use the stepbystep guides below for further detail on individual topics. Other topic guides in this series include:
1. Which of the following numbers is a natural number?
Natural numbers are the set of whole positive numbers that start at 1.
15 is a positive whole number so it is a natural number.
2. Which group of numbers are natural numbers?
Natural numbers are the set of whole positive numbers that start at 1.
So, 1, 2, 3 are natural numbers.
3. Which group of numbers represents prime numbers?
A prime number is a number that has exactly two factors, 1 and itself.
2, 3, 7 represent prime numbers because:
The factors of 2 are 1 and 2.
The factors of 3 are 1 and 3.
The factors of 7 are 1 and 7.
4. Find the missing number using the associative property.
(6 + 5) + 10 = 6 + ( \, \rule{0.5cm}{0.15mm} \, + 10)
The associative property is (a + b) + c = a + (b + c).
So, (6 + 5) + 10 = 6 + (5 + 10)
(6 + 5) + 10 = 21
6 + (5 + 10) = 21
5. Find the missing number using the commutative property.
12 \times \, \rule{0.5cm}{0.15mm} \, = 8 \times 12
The commutative property is a \times b = b \times a.
So, 12 \times 8 = 8 \times 12.
12 \times 8 = 96
8 \times 12 = 96
6. Find the missing number using the distributive property.
4 \times (2 + 9) = 8 + \, \rule{0.5cm}{0.15mm}
The distributive property is a \times (b + c) = a \times b + a \times c.
So, 4 \times (2 + 9) = 8 + 36 = 44
No, natural numbers are positive whole numbers that start with 1.
No, only positive whole numbers are natural numbers. Positive fractions and decimals are not natural numbers.
No, only the nonnegative integers starting with 1 are natural numbers.
Cardinal numbers are natural numbers used for counting. They are countable numbers.
Ordinal numbers are natural numbers used for ordering objects such as 1 st, 2 nd, 3 rd, etc…
Only the positive integers are rational numbers, not including 0. Negative numbers are not natural numbers, and fractions and decimals are not natural numbers. Natural numbers are a subset of rational numbers.
Set theory serves as a foundation for everything that is done in mathematics because it builds concepts of numbers.
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