Read the Chapter 1 Real Numbers PDF for free. This is part of the official NCERT Book for Class 10 Mathematics for the 2026-27 academic year. Students can use this book online or offline.
NCERT Book Class 10 Mathematics - Chapter 1 Real Numbers PDF
This chapter in NCERT Book Class 10 Maths Real Numbers Questions makes learning easy for Class 10 Mathematics students. Read it carefully. Also, use the NCERT Solutions for Class 10 Mathematics to check answers for all the textbook questions.
NCERT Class 10 Mathematics Chapter 1 Real Numbers PDF
• Euclid’s Division Lemma : Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.
• Euclid’s Division Algorithm to obtain the HCF of two positive integers, say c and d, c > d.
Step 1 : Apply Euclid’s division lemma to c and d, to find whole numbers q and r, such that c = dq + r, 0 ≤ r < d.
Step 2 : If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
Step 3 : Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.
• Fundamental Theorem of Arithmetic : Every composite number can be expressed as a product of primes, and this expression (factorisation) is unique, apart from the order in which the prime factors occur.
• Let p be a prime number. If p divides a2, then p divides a, where a is a positive integer.
• √2 , √3 , √5 are irrational numbers.
• The sum or difference of a rational and an irrational number is irrational.
• The product are quotient of a non-zero rational number and an irrational number is irrational. • For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
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Class 10 Mathematics Chapter 1 Real Numbers Official E-Book
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