Number Play Questions and Answers - Free PDF Download
In NCERT Solutions for Class 6 Maths Chapter 3 Number Play Exercise 3.8, you will get to work on fun number puzzles and mental math tricks! This part of your Maths book focuses on understanding number patterns, prime and composite numbers, divisibility rules, and more—all without a pen and paper.
Table of Content
If you ever get stuck on a tricky problem or feel confused about primes, factors, or mental math techniques, these Vedantu solutions will make each step clear and simple. The downloadable PDFs are perfect for revision or quick homework checks. For a quick look at your full syllabus, you can check the Class 6 Maths syllabus anytime.
Practising with these NCERT Solutions for Class 6 Maths helps you build speed, accuracy, and confidence—especially for exams! For answers from every chapter, explore all Class 6 Maths NCERT Solutions as well.
Exercise 3.8
Question 1. Write an example for each of the below scenarios whenever possible.
Could you find examples for all the cases? If not, think and discuss what could be the reason. Make other such questions and challenge your classmates.
(a) Let’s divide
90, 250 by 2
Hence to get sum more than 90,250 both numbers should be more than 45,125.
(b) To get a 6 digit sum by adding 5 digit and 3 digit, the 5 digit number should be more than 99,001.
(c) Let’s take minimum 4 digit number 1000
let’s add them
which is a 4 digit number.
Hence 6 digit sum’ from 4 digit number is impossible.
(d) Let’s take 5 digit numbers 67987 and 65783
let’s add them
which is a 6 digit number.
(e) Let’s take minimum 5 digit numbers 1000
let’s add them
which is a 5 digit number.
Hence 6 digit sum from 5 digit numbers is impossible.
(f) 5-digit -5 digit to
give a difference less than 56,503
< 56503
(g) 5-digit-3 digit = 1 008 6 (5 digit) to give a 4 digit = + 875 (3 digit)
difference = 92 11 (4 digit)
(h) 5-digit digit = 1 2 8 7 6 (5 digit) to give a 4 digit = -7865 (4 digit)
difference = 5 0 11 (4 digit)
(i) 5-digit -5 digit 7 = 645 3 (5 digit) to give a 3 digit = 76 145 (5 digit)
difference = 308 (3 digit)
(j) 5-digit -5 digit
Not possible to give 91,500
Question 2. Always, Sometimes, Never?
Below are some statements. Think, explore and find out if each of the statement is ‘Always true’, ‘Only sometimes true’ or ‘Never true’. Why do you think so? Write your reasoning; discuss this with the class.
(a) 5-digit number + 5-digit number gives a 5-digit number
(b) 4-digit number + 2-digit number gives a 4-digit number
(c) 4-digit number + 2-digit number gives a 6-digit number
(d) 5-digit number – 5-digit number gives a 5-digit number
(e) 5-digit number – 2-digit number gives a 3-digit number
Solution:
Benefits of NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.8
Enhances problem-solving speed through mental math exercises.
Develops a strong foundation in number theory.
Improves understanding of number properties such as divisibility and multiples.
Strengthens logical reasoning by exploring number patterns and sequences.
Prepares students for advanced topics in mathematics.
Encourages independent thinking and mental calculations.
Class 6 Maths Chapter 3: Exercises Breakdown
Important Study Material Links for Maths Chapter 3 Class 6
Conclusion
Chapter 3: Number Play is an essential part of the Class 6 Maths curriculum that fosters an understanding of numbers and their properties. Exercise 3.8, focused on Mental Math, plays a key role in boosting mental agility and calculation speed. By mastering this chapter, students can improve their mathematical fluency and problem-solving skills, which will benefit them in both academic and real-life situations.
Chapter-wise NCERT Solutions Class 6 Maths
After familiarising yourself with the Class 6 Maths Chapters Question Answers, you can access comprehensive NCERT Solutions from all Class 6 Maths textbook chapters.
Related Important Links for Class 6 Maths
Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6-
FAQs on NCERT Solutions For Class 6 Maths Chapter 3 Number Play Exercise 3.8 - 2025-26
1. Where can I find reliable, step-by-step NCERT Solutions for Class 6 Maths Chapter 3 for the 2025-26 session?
You can find comprehensive and accurate NCERT Solutions for Class 6 Maths Chapter 3, Number Play, on Vedantu. These solutions are prepared by subject matter experts and follow the latest CBSE 2025-26 syllabus. Each answer provides a detailed, step-by-step method to ensure students understand the logic behind solving each problem. For a complete learning experience, you can also explore NCERT Solutions for Class 6 for all subjects.
2. How do you find the HCF of two numbers using the prime factorisation method as shown in NCERT Class 6 Maths Chapter 3?
To find the Highest Common Factor (HCF) using the prime factorisation method as per the NCERT textbook, you should follow these steps:
Step 1: Find the prime factors of each number separately. You can learn more about this on the Prime Factors page.
Step 2: Identify the common prime factors from all the numbers.
Step 3: Multiply these common prime factors together. The resulting product is the HCF of the given numbers.
3. What is the correct method to find the LCM of multiple numbers as per the NCERT solutions for Chapter 3?
The NCERT solutions for Chapter 3 explain the common division method to find the Least Common Multiple (LCM). The steps are:
Step 1: Arrange the given numbers in a row, separated by commas.
Step 2: Divide the numbers by the smallest prime number that can divide at least one of them.
Step 3: Write the quotients and any undivided numbers in the next row.
Step 4: Repeat this process until all the numbers in the last row are 1.
Step 5: The LCM is the product of all the prime divisors used in the process. This concept is further detailed on the HCF and LCM page.
4. How do I apply the divisibility test for 11 to solve questions in Class 6 Maths Chapter 3?
To apply the divisibility test for 11 as explained in the NCERT solutions, follow this procedure:
First, find the sum of the digits at the odd places (from the right).
Next, find the sum of the digits at the even places (from the right).
Calculate the difference between these two sums.
If the difference is either 0 or a multiple of 11, the original number is divisible by 11. This method is essential for quickly checking factors without performing long division.
5. What key topics are covered in the NCERT Solutions for Class 6 Maths Chapter 3, Number Play?
The NCERT Solutions for Class 6 Maths Chapter 3 cover several fundamental concepts related to numbers. The main topics you will find step-by-step solutions for include:
- Factors and Multiples
- Prime and Composite Numbers
- Tests for Divisibility of Numbers (for 2, 3, 4, 5, 6, 8, 9, 10, 11)
- Common Factors and Common Multiples
- Prime Factorisation
- Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
6. Why is the prime factorisation method a reliable way to find both HCF and LCM in NCERT Chapter 3 problems?
The prime factorisation method is reliable because it breaks down each number into its most fundamental components: its prime factors. This unique set of prime factors acts like a 'fingerprint' for the number. For the HCF, you find the shared 'fingerprint' components (common factors). For the LCM, you gather all unique 'fingerprint' components to the highest power, ensuring the result is a multiple of all original numbers. This systematic approach eliminates guesswork and works for any set of numbers, as explained in our detailed prime factors guide.
7. What is a common mistake students make when finding the HCF and LCM, and how do the NCERT Solutions help avoid it?
A common mistake is confusing the methods for HCF and LCM. For HCF, students might multiply all prime factors instead of only the common ones. For LCM, they might miss taking the highest power of a repeated prime factor. The NCERT Solutions help prevent this by providing clear, step-by-step instructions for each method, highlighting the specific rules for selecting and multiplying factors for both HCF and LCM, ensuring conceptual clarity.
8. How do the NCERT Solutions for Chapter 3 explain the relationship between the HCF, LCM, and the product of two numbers?
The NCERT Solutions for Chapter 3 demonstrate a crucial property connecting HCF and LCM for any two given numbers. The relationship is: Product of two numbers = HCF of the numbers × LCM of the numbers. The solutions often include verification problems where you first calculate the HCF and LCM independently and then show that their product equals the product of the original two numbers. This formula is a useful tool for checking answers and solving problems where one of the four values is unknown. For more details, refer to Vedantu's page on HCF and LCM.
9. How can the concepts of HCF and LCM from Chapter 3 be applied to solve real-world problems, as hinted in the NCERT exercises?
The NCERT exercises often use word problems to show real-world applications of HCF and LCM. Here's how they apply:
HCF (Highest Common Factor) is used when you need to find the largest size to divide things into equal parts. For example, finding the largest measuring tape that can measure different lengths exactly.
LCM (Lowest Common Multiple) is used when you need to find when events will happen at the same time again. For example, finding when two bells ringing at different intervals will ring together. Problems in exercises like Exercise 3.7 often feature such scenarios.
10. The NCERT solutions for Chapter 3 cover both factors and multiples. How does the approach to finding common factors differ from finding common multiples?
The approach differs fundamentally in direction and scope:
Finding Common Factors: This is a process of division. You find all the numbers that divide your given numbers without a remainder. The list of factors for any number is finite, ending at the number itself. The goal is often to find the Highest Common Factor.
Finding Common Multiples: This is a process of multiplication. You find the numbers that appear in the multiplication tables of your given numbers. The list of multiples for any number is infinite. The goal is to find the Lowest Common Multiple.
Essentially, factors are 'smaller or equal to' the number, while multiples are 'larger or equal to' it. The NCERT solutions use methods like listing and prime factorisation to clarify these distinct processes while Playing with Numbers.
