Download Finding Common Ground – NCERT Class 7 Maths Chapter 11 PDF from the new NCERT Class 7 Maths book Ganita Prakash (2026-27). Read the chapter online or download the free PDF. The Highest Common Factor (HCF) of two or more numbers is the greatest of their common factors. It is also called the Greatest Common Divisor (GCD).
Finding Common Ground PDF – Chapter 11 of Ganita Prakash (Part II)
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 11 PDF | Finding Common Ground | View PDF |
| Full book | NCERT Class 7 Maths – Ganita Prakash | View Book |
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What Is in Finding Common Ground? (Class 7 Maths Chapter 11)
- The Highest Common Factor (HCF) of two or more numbers is the greatest of their common factors. It is also called the Greatest Common Divisor (GCD).
- The Lowest Common Multiple (LCM) is the least of their common multiples. There is no greatest common multiple — the list of common multiples never ends.
- Every factor of a number is a subpart of its prime factorisation. So a common factor must be a subpart of both factorisations, and the HCF is the largest such subpart.
- HCF rule: keep only the primes common to all the numbers, each taken the minimum number of times it occurs. LCM rule: keep every prime that occurs anywhere, each taken the maximum number of times.
- The division method for two numbers divides both numbers by a common factor again and again. The left column multiplies to the HCF; the left column together with the last row multiplies to the LCM.
- For any two numbers, HCF × LCM = product of the two numbers. The common primes go into the HCF, the leftover primes into the LCM, and together they rebuild the product.
- A claim made without proof is a conjecture. One counterexample is enough to disprove it. A statement that holds in every case is a generalisation.
Quick revision – Finding Common Ground
| Idea | What it means | Example from the chapter | Result |
|---|---|---|---|
| Common factor | A number that divides both numbers | Factors of 12 and 16 | 1, 2, 4 |
| HCF (GCD) | The greatest common factor | 12 and 16 (Sameeksha’s room) | 4 ft tile |
| Prime factorisation | Rewrite composite factors till only primes remain | 90 = 2 × 3 × 3 × 5 | Unique, up to order |
| Division method | Divide by a prime, bring the quotient down, repeat | 105 → 3, 5, 7 | 105 = 3 × 5 × 7 |
| Factor = subpart | Any group of the prime factors multiplies to a factor | 840 = (2 × 2 × 7) × (2 × 3 × 5) | 28 is a factor |
| HCF by primes | Common primes, each taken the minimum number of times | 30 = 2 × 3 × 5; 72 = 2 × 2 × 2 × 3 × 3 | HCF = 6 |
| LCM by primes | All primes, each taken the maximum number of times | 96 = 2 × 2 × 2 × 2 × 2 × 3; 360 = 2 × 2 × 2 × 3 × 3 × 5 | LCM = 1440 |
| Division method for two numbers | Divide both by a common factor, repeat | 630, 770 → 2, 5, 7 → 9, 11 | HCF 70, LCM 6930 |
| One number is a factor of the other | Then it is the HCF and the other is the LCM | N and 5n | HCF n, LCM 5n |
| Co-prime numbers | No common prime factor | 7 and 11 | HCF 1, LCM 77 |
| Product property | HCF × LCM = the product of the two numbers | 105 × 95 = 5 × (3 × 5 × 7 × 19) | HCF 5, LCM 1995 |
| Conjecture | A claim made without proof; one counterexample kills it | “Larger number → longer prime factorisation” | 121 = 11 × 11 |
Old NCERT vs New – Class 7 Maths
This chapter is from Ganita Prakash, the new NCERT Class 7 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Mathematics”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Ganita Prakash:
Finding Common Ground – Overview
| Class | Class 7 |
| Subject | Maths |
| Book | Ganita Prakash – new NCERT book |
| Part | Part II |
| Chapter | 11 of 15 – Finding Common Ground |
| Book pages | Part II, 47 – 66 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 7 Maths Chapter 11 – FAQs
Where can I download Finding Common Ground Class 7 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 7 Maths Chapter 11 about?
The Highest Common Factor (HCF) of two or more numbers is the greatest of their common factors. It is also called the Greatest Common Divisor (GCD).
Is Finding Common Ground from the new NCERT Class 7 Maths book?
Yes. It is chapter 11 of ganita prakash (part ii), the new NCERT Class 7 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 7 Maths Chapter 11?
Open the NCERT Solutions link above for answers to the exercise questions.