Prime factorisation, HCF and LCM, the HCF × LCM product rule and proofs that a number is irrational. Our own step-by-step solutions to Exercises 1.1 and 1.2, one page per exercise, set out for step marks.
Each exercise has its own page with every question solved step by step. Pick the one you are on.
What it tests. Fundamental Theorem of Arithmetic: every composite number is a product of primes in exactly one way. HCF = product of the smallest powers of common primes; LCM = product of the greatest powers of all primes.
What it tests. Proof by contradiction: assume the number is rational, write it as a fraction in lowest terms, and reach a contradiction. Uses the fact that if a prime p divides a², then p divides a.
Real Numbers has 40 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
Also useful: free MCQs and case studies for Real Numbers · Class 10 formula sheet · official CBSE board and sample papers · our sample papers with marking scheme · the Route to 95 plan
Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.