Class 6 Maths Chapter 3 Exercise 3.2, will introduce students to important number concepts like factors, multiples, and finding common factors and multiples. These topics introduce concepts essential for divisibility, LCM and HCF it is important for problem solving involving numbers.
The questions of the exercise are relevant to the CBSE syllabus and NCERT syllabus. Regular practice will reinforce their conceptual understanding and clarity so as to improve accuracy in solving problems related to numbers. This exercise can help students prepare for school assessments and competition assessments such as Olympiads.
The NCERT Solutions that are detailed and easy to understand in a free downloadable PDF format. Each NCERT Solution is presented step by step, to help students understand the logic and method behind the answers. This resource can help students with self-study, revision and a quick way to solve any doubts or misconceptions they may have.
The NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.2 focuses on the factors and multiples, and it helps you with how to find them easily. Our solutions will help you learn more effectively so you can perform better on your exam. Click below for the free PDF of the solutions:
1. Colour or mark the supercells in the table below.
Sol.
2. Fill the table below with only 4 -digit numbers such that the supercells are exactly the coloured cells.
Sol.
3. Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
Sol.
4. Out of the 9 numbers, how many supercells are there in the table above?
Sol. Out of 9 numbers, there are 5 supercells in the above table.
6. Find out how many supercells are possible for different numbers of cells.
Do you notice any pattern? What is the method to fill a given table to get the maximum number of supercells? Explore and share your strategy.
Sol. If there are n odd cells then maximum number of supercells =n+1/2
If there are n even cells then maximum number of supercells =n/2
Yes, there is a pattern. Alternate cells can be supercells.
Method to fill a given table to get the maximum number of supercells.
Make first cell as supercell. After that each alternate cell is to be made supercell.
7. Can you fill a supercell table without repeating numbers such that there are no supercells? Why or why not?
Sol. No, it is not possible to fill a supercell table without repeating numbers such that there are no supercells. As there are two cases:
Case I: If we fill the cells in descending order then the first cell can be supercell.
Case II: If we fill the cells in ascending order then the last cell will be supercell. If we don't follow any order, then there will definitely at least one supercell.
8. Will the cell having the largest number in a table always be a supercell? Can the cell having the smallest number in a table be a supercell? Why or why not?
Sol. Yes, the cell having the largest number in a table always be a supercell (considering that the numbers in all the cells are different) because if it is a corner cell, then the number adjacent to it (i.e., either second cell or second last cell) will be smaller than it. If it is in between then both its adjacent numbers would be smaller than it.
No, the smallest number cannot be a supercell. A supercell has to be bigger than all its neighbours. Since it's the smallest, it can't be bigger than any neighbouring numbers, so it can't be a supercell.
9. Fill a table such that the cell having the second largest number is not a supercell.
Sol.
10. Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a supercell. Is it possible?
Sol.
11. Make other variations of this puzzle and challenge your classmates.
Sol. We can also make other variations of given puzzle as:
A cell will be coloured if the number in it is smaller than its adjacent cells.
(Session 2025 - 26)