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Number Theory Basics: Real Numbers & Number System
Rating: 4.3 out of 5(21 ratings)
1,739 students

Number Theory Basics: Real Numbers & Number System

Learn number theory from scratch: real numbers, HCF, LCM, Euclid's lemma, and rational and irrational numbers.
Created byLetstute .... Make it Easy
Last updated 8/2026
English

What you'll learn

  • They will learn origin and history of numbers
  • Category of real numbers, HCF, Euclid's division algorithm

Explore related topics

Course content

2 sections • 17 lectures • 2h 21m total length

  • Introduction - Real numbers4:53

    This is an introductory session on the topic ' Real Numbers' where you will learn about Number Systems and their properties in just than 5 minutes.
    Watch this session and familiarise yourself with the following terms:
    1) Whole Numbers
    2) Prime Numbers
    3) Composite Numbers
    4) Rational Numbers
    5) Irrational Numbers.
    These basic concepts will help you understand the further topics better.

  • Origin and History of numbers9:58

    If you think Math is never needed or has no importance then try to imagine the world without numbers.

    Watch this video on Origin and History of Numbers and explore the knowledge.

  • How to find the Least common multiple (LCM)9:43

    Least Common Multiple (LCM) is the smallest number which is exactly divisible by all the given numbers.

    But how do we find the LCM of any given number?
    Get step wise explanation on how to find LCM by Prime Factorization Method in less than 10 minutes.

  • Highest common factor(HCF) and Euclid's division lemma9:51

    Gain an understanding of an important concept in number theory- The Euclid's Division Lemma and learn its application in finding out The Highest Common Factor (HCF).
    This video covers the following topics in less than 10 minutes:
    1) Factors
    2) Divisors
    3) Highest Common Factor / Greatest Common Divisor
    4) Method of Finding HCF
    6) Euclid's Division Lemma
    7) Euclid's Division Algorithm.
    So, Understand the core concept and learn its logical application.

  • Decimal form of rational numbers8:16

    Any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q is called Rational Number.

    But can this be written in decimal form?
    Watch this session to know how a fraction can be converted into a decimal form.
    The concept is explained stepwise in an easy to understand manner by in 10 minutes.

  • Decimals to fractions - Real numbers10:51

    In this session will learn about converting Decimal numbers into ratio form.

    1. Converting fractional form to decimal numbers conversion

    2. Converting decimal numbers to fractional form.

    a. Finite decimal to fractional form

    b. Infinite decimal to fractional form.


  • Irrational numbers and proof of root 2 is irrational12:53

    Irrational Numbers are any numbers which cannot be written as a fraction.

    Watch this session to learn:
    1)Few properties of Irrational Numbers
    2)Examples of Irrational Numbers
    3)How to proove  √2 is an irrational number.
    All the concepts are explained in a logical and easy manner in 13minutes.

  • Finding rational numbers10:16

    In this session will learn about finding the rational numbers 3 different methods.

    1. Rationals numbers that are equidistant.

    2. Rationals numbers by finding the midpoints.

    3. Rationals numbers by finding the difference.


  • Quiz - 1 (Real Numbers)5:31

    This is a Quiz video that will test your knowledge on the topic and help you understanding the concept in depth.

  • Quiz - 2 (Real Numbers)5:28

    This is a Quiz video that will test your knowledge on the topic and help you understanding the concept in depth.

Requirements

  • No prior knowledge or experience require

Description

Every calculation you've ever done rests on one thing: how numbers actually work.

This course takes you into number theory, the branch of mathematics behind real numbers and the number system, and builds your understanding from the ground up. From the origin and history of numbers to rational and irrational numbers, HCF and Euclid's division lemma, LCM, and converting between decimals and fractions, you'll see the logic that holds our entire number system together.

It's designed for school students studying real numbers and number systems, and for any learner who wants a clear, solid grasp of the fundamentals. Every topic comes with explanatory videos, worked problem-solving, quiz videos, and downloadable PDF assessments.

What you'll learn:

  • Introduction to real numbers

  • The origin and history of numbers

  • Highest common factor (HCF) and Euclid's division lemma

  • The decimal form of rational numbers, and finding rational numbers

  • How to find the least common multiple (LCM)

  • Converting decimals to fractions

  • Irrational numbers

  • Quiz videos and PDF assessments to test your understanding

Who this course is for:

  • School students with real numbers or number systems in their curriculum

  • Learners who want a strong foundation in number theory

  • Teachers looking for clear ways to explain the topic

Understand the numbers behind the mathematics. Enroll now and build your foundation with confidence.

Who this course is for:

  • Anyone wants to learn Real numbers and Number system in detail
  • Students who are appearing for Competitive exams

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