NCERT Solutions Class 10 Maths Chapter 1 — Real Numbers#

Chapter 1 of Class 10 Maths introduces the Fundamental Theorem of Arithmetic — every composite number can be expressed as a product of primes in a unique way. You will use it to find the HCF and LCM of numbers, and prove that numbers like √2, √3 and √5 are irrational.

Exercises#

• Exercise 1.1 — HCF and LCM using prime factorisation and the Fundamental Theorem of Arithmetic (7 questions)
• Exercise 1.2 — Proofs of irrationality (3 questions)

What you will learn#

• Write any composite number as a product of primes, and why that factorisation is unique (the Fundamental Theorem of Arithmetic).
• Find the HCF and LCM of two or three numbers from their prime factorisations.
• Use the link between the HCF, the LCM and the product of two numbers.
• Prove that numbers such as √2, √3, √5 and 3 + 2√5 are irrational, by contradiction.

Key formulas and results#

• $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$ for any two positive integers $a$ and $b$.
• If a prime $p$ divides $a^2$, then $p$ divides $a$ — the key step in every irrationality proof.

Read and revise#

• Class 10 Maths Notes — Real Numbers: every definition, formula and method in short.
• All Class 10 Maths formulas on one page.
• NCERT Class 10 Maths Chapter 1 (PDF) — the textbook chapter itself, and all Class 10 Maths chapters.

Frequently asked questions#