Class 7 Maths Ganita Prakash Part 2 Chapter 3 Finding Common Ground NCERT Solutions

Welcome to the complete NCERT Solutions for Class 7 Maths Ganita Prakash Part 2, Chapter 3 – Finding Common Ground. In this blog, you will find step-by-step solutions to the important questions from the chapter, including all the Figure It Out questions, explained in a simple and easy-to-understand manner.

These solutions are designed to help students understand the mathematical concepts clearly, develop logical thinking, and solve problems confidently. Whether you are looking for exercise-wise solutions, help with challenging questions, or a quick revision before your examination, this blog will guide you through the chapter.

Explore the complete Class 7 Maths Chapter 3 Finding Common Ground NCERT Solutions and strengthen your mathematical understanding with clear explanations and accurate answers. My Youtube Channel name is CBSE Worldz where you can watch video solutions and chapter explanation videos.

Figure it Out Page: 51

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Q: List all the factors of the following numbers:

(a) 90

(b) 105

(c) 132

(d) 360 (this number has 24 factors)

(e) 840 (this number has 32 factors)

Solution:

a) 90
90 = 1 × 90
90 =2 × 45
90 =3 × 30
90 =5 × 18
90 =6 × 15
90 =9 × 10
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

(b) 105
105 = 1 × 105
105 =3 × 35
105 =5 × 21
105 =7 × 15
Factors of 105 = 1, 3, 5, 7, 15, 21, 35, 105

(c) 132
132 = 1 × 132
132 = 2 × 66
132 = 3 × 44
132 = 4 × 33
132 = 6 × 22
132 = 11 × 12
Factors of 132 = 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132

(d) 360
360 = 1 × 360
360 = 2 × 180
360 = 3 × 120
360 = 4 × 90
360 = 5 × 72
360 = 6 × 60
360 = 8 × 45
360 = 9 × 40
360 = 10 × 36
360 = 12 × 30
360 = 15 × 24
360 = 18 × 20
Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

Figure it Out Page: 53

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Find the common factors and the HCF of the following numbers:

(a) 50, 60

(b) 140, 275

(c) 77, 725

(d) 370, 592

(e) 81, 243

Solution:

 

Figure it Out Page: 54

1. Find the HCF of the following numbers:

(a) 24, 180

(b) 42, 75, 24

(c) 240, 378

(d) 400, 2500

(e) 300, 800

Solution:

2. Consider the numbers 72 and 144. Suppose they are factorised into composite numbers as: 72 = 6 × 12 and 144 = 8 × 18. Seeing this, can one say that these two numbers have no common factor other than 1? Why not?

Ans: No, we cannot say that 72 and 144 have no common factor other than 1. It is because we cannot use composite factorisation to decide common factors. Only prime factorisation correctly shows common factors.