A fast, one-glance recap of Class 10 Maths Chapter 1 (Real Numbers) — for the full worked explanations, see the Solutions. These Class 10 Mathematics Chapter 1 notes are ideal for quick revision just before exams.
Last Updated: October 24, 2026
Common Mistakes Students Make in Real Numbers
- HCF/LCM formula misuse: HCF × LCM = product of the two numbers only works for exactly two numbers, not three or more.
- Euclid’s division algorithm slips: misidentifying the larger/smaller number, or losing track partway through the repeated division steps.
- Incomplete irrationality proofs: not clearly stating the initial assumption or properly justifying the contradiction when proving a number like √2 is irrational.
- Prime factorisation errors: missing a prime factor or miscounting the power of a repeated one.
Why This Chapter Matters
Real Numbers is one of the standard chapters in the CBSE/NCERT Class 10 Maths syllabus and questions from it appear regularly in board exams, in formats ranging from 1-mark objective questions to longer 3-5 mark descriptive or numerical questions. Because the concepts here often build on earlier chapters (and feed into later ones), a solid grip on this chapter also makes the rest of the Maths syllabus easier to follow.
Revision Notes: Real Numbers
- Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b
- Euclid’s Division Algorithm: repeatedly apply the lemma to find HCF — the last non-zero remainder’s divisor is the HCF
- Fundamental Theorem of Arithmetic: every composite number factorises into primes uniquely (order aside)
- HCF × LCM = product of the two numbers (two numbers only, not three or more)
- Proving irrationality: assume rational (p/q, coprime, q≠0) → show p and q share a common factor → contradiction
- Know by heart: √2, √3, √5, and √p for any prime p are irrational; 6n never ends in 0 (no factor of 5)
Keep Going
Full Solutions · Extra Questions (HOTS) · Formulas Handbook
How to Use These Notes
These revision notes are meant for quick recall in the last few days before an exam or unit test — they are not a substitute for first reading the full chapter and working through examples in the NCERT textbook. A good routine is: read the chapter once, solve the in-text and end-of-chapter questions using the linked Solutions, then come back to this page a day or two before the exam to refresh the key definitions and formulas without re-reading the whole chapter.
Class 10 Mathematics Chapter 1 – Solutions and Important Questions
Need full answers or more practice? See the Class 10 Mathematics Chapter 1 Solutions and Class 10 Mathematics Chapter 1 Extra Questions.
