NCERT Class 7 Mathematics Ganita Prakash-II: Chapter 3 — Finding Common Ground
This chapter, 'The Greatest of All,' from NCERT's Class 7 Mathematics Ganita Prakash-II, introduces the concept of the Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD). It uses practical examples like tiling a room and packing rice to illustrate how to find the largest possible square tile size or the maximum weight per bag, which corresponds to the HCF of the dimensions or quantities. Students learn to identify common factors of numbers and select the greatest among them to solve real-world problems efficiently. The chapter also revisits the 'Jump Jackpot' game from Grade 6 to reinforce the understanding of HCF as the longest jump size. This foundational concept is crucial for various mathematical applications and problem-solving in CBSE curriculum.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 7 |
| Subject | Mathematics |
| Book | Ganita Prakash-II |
| Chapter | Chapter 3 — Finding Common Ground |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 667 |
Learning outcomes
- Understand the concept of factors and common factors.
- Define and identify the Highest Common Factor (HCF) or Greatest Common Divisor (GCD) of two or more numbers.
- Apply the HCF concept to solve real-world problems involving dimensions and quantities.
- Relate HCF to finding the largest possible size for tiling or the maximum weight for packing.
- Connect HCF to the concept of the longest jump size in a number line.
Vocabulary
| Word | Meaning |
|---|---|
| Factor | A number that divides another number exactly without leaving a remainder. |
| Common Factor | A number that is a factor of two or more numbers. |
| Highest Common Factor (HCF) | The largest number that is a common factor of two or more numbers. |
| Greatest Common Divisor (GCD) | Another name for the Highest Common Factor. |
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Practice questions
- What are the factors of 18? Answer: 1, 2, 3, 6, 9, 18
- Find the common factors of 15 and 25. Answer: 1, 5
- What is the HCF of 10 and 20? Answer: 10
- If a room is 10 ft by 15 ft, what is the largest square tile size (in whole feet) that can be used to tile the floor exactly? Answer: 5 ft
Frequently asked questions
What is the main concept taught in NCERT Class 7 Mathematics Chapter 3?
The chapter 'The Greatest of All' teaches the concept of the Highest Common Factor (HCF) or Greatest Common Divisor (GCD).
How is HCF related to tiling a room?
The HCF of the room's length and width gives the largest possible whole number side length for square tiles that can cover the floor exactly.
What does HCF mean in the context of packing rice?
The HCF of the weights of rice from different farms gives the maximum equal weight each bag can hold, minimizing the number of bags used.
Is HCF the same as GCD?
Yes, HCF (Highest Common Factor) and GCD (Greatest Common Divisor) are two names for the same mathematical concept.
Can HCF be a fractional number?
While factors can be fractional, the HCF is typically defined for integers. In practical problems like tiling, the side length of the tile is usually a whole number, which is the HCF.
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Topics covered
NCERT Class 7 Mathematics — Ganita Prakash-II — Chapter 3 — Finding Common Ground. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.