Chapter 1: Real Numbers - Solutions
Chapter solutions are on NCERT Archive
Step-by-step solutions for this chapter now live on NCERT Archive, along with the chapter itself. Use the buttons below to open them.
About Chapter 1 (Real Numbers)
Chapter 1 (Real Numbers) is chapter 1 of 14 in the new edition of NCERT Class 10 Mathematics, a textbook for Class 10 students at the Secondary stage. This is the new edition, the textbook brought out under the NEP 2020 / NCF-SE 2023 syllabus rollout.
Chapter 1 revisits the properties of real numbers built up in earlier classes and develops two central results: Euclid's Division Lemma and the Fundamental Theorem of Arithmetic. Together these tools are used across the chapter's two exercises to find the HCF and LCM of integers using Euclid's division algorithm and prime factorisation.
It is the opening chapter of the book and is followed by Chapter 2 (Polynomials).
Topics covered
- Euclid's Division Lemma
- Euclid's Division Algorithm
- The Fundamental Theorem of Arithmetic
- HCF and LCM by prime factorisation
What the solutions on NCERT Archive include
NCERT Archive is our dedicated site for NCERT textbooks and solutions, Class 1 to 12. The solutions page for Chapter 1 (Real Numbers) there gives chapter-wise answers to the questions of NCERT Class 10 Mathematics, written to follow the order of the textbook, and links back to the chapter itself. Use the buttons above to go to it.
How to study Real Numbers
- Read the worked examples before the exercises and copy out each step in your own hand.
- Attempt every exercise question yourself first; open the solution only to check your method or when you are stuck.
- Keep a short list of formulas and definitions from the chapter and revise it before tests.
- Redo the questions you got wrong after a day or two, without looking at the solution.
Frequently Asked Questions
Which book is Chapter 1 (Real Numbers) of Class 10 Mathematics from?
It is from the new edition of NCERT Class 10 Mathematics. The book has 14 chapters, and this is chapter 1.
Where can I find the solutions for Chapter 1 (Real Numbers) of Class 10 Mathematics?
On NCERT Archive. Press the "Open Chapter Solutions" button on this page and you will land on the solutions page for this chapter there.
Is this the new edition or the old edition?
This page is for the new edition. If your school still uses the earlier textbook, use the Old Edition switch at the top of the page.
Is it free to use?
Yes. Scholar Donkey and NCERT Archive are free to use and need no login.