Select your language

Suggested languages for you:
Log In Start studying!
StudySmarter - The all-in-one study app.
4.8 • +11k Ratings
More than 3 Million Downloads
Free
|
|

All-in-one learning app

  • Flashcards
  • NotesNotes
  • ExplanationsExplanations
  • Study Planner
  • Textbook solutions
Start studying

Natural Numbers

Natural Numbers

A natural number is a positive whole number from 1 onwards. Negative numbers are not considered natural numbers. Some examples are 1, 67, 450, 23005 and 2000000. Natural numbers are often represented on a number line;

Natural Numbers Number line example StudySmarterNatural Number Line, Thomas-Gay, StudySmarter Originals

Number classes

Natural numbers can also be part of other number classes, and the diagram below shows how they are all related;

Natural Numbers Number Classes StudySmarterNumber Classes, Thomas-Gay - StudySmarter Originals

Properties of natural numbers

Natural numbers have four different properties;

  • Closure property – this means that when two or more natural numbers are multiplied or added together, it will result in a natural number. For example, or .

  • Associative property – suggests that when three natural numbers are added or multiplied together, it will result in the same answer no matter how they are grouped. For example, 3 + (2 + 5) = 10 and (3 + 2) + 5 = 10. This also works when they are multiplied, and .

  • Commutative property – this property says that when two natural numbers are multiplied or added together, they will result in the same answer no matter their order. For example, 4 + 8 = 12 and 8 + 4 = 12. This also works when they are multiplied, and .

  • Distributive property – when three natural numbers are being multiplied using brackets, you can also do this by multiplying the numbers separately. For example, 5 (2 + 3) = 25 and .

What is the natural numbers symbol?

A set of natural numbers is often represented by the symbol .

How to find the sum of natural numbers

The list of natural numbers creates an arithmetic sequence. There is a formula that you can use to help you find the sum of a sequence of natural numbers:

In the above formula, n represents the number of terms. The sequence will start with 1. It is also important to note that the sum of all natural numbers is infinity.

Sigma , is a notation used to represent the sum of terms

Find the sum of the first 50 natural numbers.

To do this, you would first start by looking at your formula, identifying the n from the question and substituting it into the formula;

Since you are finding the sum of the first 50 terms, n = 50, therefore;

Now you can simply solve the formula to find your answer;

Find the sum of the first 100 natural numbers.

As before, you need to identify the n for the formula from the question. In this case, n=100, and now you can substitute it into the formula and solve the question:

Learn more about arithmetic Sequences and Series.

Natural Numbers - Key takeaways

  • A natural number is a positive whole number higher than 1.
  • Natural numbers are often represented on a number line.
  • The notation is used to represent a set of natural numbers.
  • The formula can be used to find the sum of the first n terms of natural numbers.

Frequently Asked Questions about Natural Numbers

Natural numbers are positive whole numbers from 1 onwards.

The difference between natural and whole numbers is that whole numbers include 0, whereas natural numbers start from 1. 

Consecutive natural numbers are numbers that follow one another, for example, 1, 2, 3, 4, 5, 6.

Final Natural Numbers Quiz

Question

What is a natural number?

Show answer

Answer

A positive whole number.

Show question

60%

of the users don't pass the Natural Numbers quiz! Will you pass the quiz?

Start Quiz

Discover the right content for your subjects

No need to cheat if you have everything you need to succeed! Packed into one app!

Study Plan

Be perfectly prepared on time with an individual plan.

Quizzes

Test your knowledge with gamified quizzes.

Flashcards

Create and find flashcards in record time.

Notes

Create beautiful notes faster than ever before.

Study Sets

Have all your study materials in one place.

Documents

Upload unlimited documents and save them online.

Study Analytics

Identify your study strength and weaknesses.

Weekly Goals

Set individual study goals and earn points reaching them.

Smart Reminders

Stop procrastinating with our study reminders.

Rewards

Earn points, unlock badges and level up while studying.

Magic Marker

Create flashcards in notes completely automatically.

Smart Formatting

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.