Number Play Questions and Answers - Free PDF Download
Chapter 3 Number Play of Class 6 Maths, students continue their exploration of number properties through Exercise 3.4. This exercise focuses on finding the divisibility of numbers and understanding how these rules help in simplifying complex calculations. The NCERT Solutions for Exercise 3.4 provide detailed explanations and step-by-step methods to ensure students understand the core concepts easily. Vedantu's solutions make learning enjoyable while also helping students improve their performance in Maths.
Table of Content
Our Class 6 Maths NCERT Solutions PDF breaks the lesson into easy-to-understand explanations, making learning fun and interactive. Students will develop essential language skills with engaging activities and exercises. Check out the revised CBSE Class 6 Maths Syllabus and start practising the Maths Class 6 Chapter 3.
Glance on Class 6 Number Play Ex 3.4 Number Play
Understanding divisibility rules for different numbers.
Applying divisibility rules to simplify calculations.
Solving problems based on divisibility.
Learning how divisibility helps in factorisation.
Using examples to strengthen understanding of divisibility.
FAQs on NCERT Solutions For Class 6 Maths Chapter 3 Number Play Exercise 3.4 - 2025-26
1. What are the main topics for which I can find solutions in NCERT Class 6 Maths Chapter 3, Playing with Numbers?
The NCERT Solutions for Class 6 Maths Chapter 3, Playing with Numbers, provide step-by-step methods for solving problems related to:
Factors and Multiples: Finding all factors and first few multiples of a number.
Prime and Composite Numbers: Identifying numbers as prime or composite.
Tests for Divisibility: Applying divisibility rules for 2, 3, 4, 5, 6, 8, 9, 10, and 11.
Prime Factorisation: Breaking down numbers into their prime factors.
HCF and LCM: Calculating the Highest Common Factor and Lowest Common Multiple. You can get a complete overview of the concepts from the NCERT Solution for Class 6 Maths Chapter 3 Number Play page.
2. How do the NCERT solutions explain the step-by-step method to find the Highest Common Factor (HCF) using prime factorisation?
The NCERT Solutions for Chapter 3 demonstrate the following steps to find the HCF using prime factorisation:
Step 1: Find the prime factorisation of each given number.
Step 2: Identify the common prime factors that appear in the factorisation of all the numbers.
Step 3: Multiply these common prime factors together. The resulting product is the HCF of the given numbers. For more details, you can refer to resources on finding the HCF (Highest Common Factor).
3. What is the correct method for finding the Lowest Common Multiple (LCM) as shown in the Chapter 3 solutions?
The NCERT Solutions for Class 6 Maths Chapter 3 explain the common division method for finding the LCM, which involves these steps:
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 the numbers exactly.
Step 3: Write the quotients and any undivided numbers in the next row.
Step 4: Repeat the process until the quotients in the last row are all 1.
Step 5: The LCM is the product of all the prime divisors used in the process. For further clarification, explore resources on HCF and LCM.
4. How do I decide whether to use HCF or LCM to solve a word problem from Chapter 3?
To decide whether to use HCF or LCM, look for these keywords and contexts in the problem:
Use HCF (Highest Common Factor) if the problem involves finding the greatest number, maximum capacity, or largest size for splitting things into equal groups or rows. For example, finding the largest tape to measure lengths exactly.
Use LCM (Lowest Common Multiple) if the problem involves finding the smallest number, minimum time, or when events will happen together again. For example, finding when two bells ringing at different intervals will ring together.
5. Why is the number 1 considered neither prime nor composite in the NCERT textbook?
The NCERT textbook defines numbers based on their factors. A number is:
Prime if it has exactly two factors: 1 and the number itself (e.g., 5 has factors 1 and 5).
Composite if it has more than two factors (e.g., 6 has factors 1, 2, 3, and 6).
The number 1 has only one factor, which is 1. Since it does not meet the criteria for being prime (exactly two factors) or composite (more than two factors), it is a unique number that is classified as neither. You can learn more about Prime and Composite Numbers here.
6. How do the solutions for Chapter 3 explain the divisibility test for 11?
The step-by-step method to check for divisibility by 11 is as follows:
Step 1: Find the sum of the digits at odd places (from the right).
Step 2: Find the sum of the digits at even places (from the right).
Step 3: Calculate the difference between these two sums.
Step 4: If the difference is either 0 or a multiple of 11, the original number is divisible by 11.
7. The NCERT solutions state that if a number is divisible by two co-prime numbers, it is divisible by their product. Why doesn't this rule work for numbers that are not co-prime, like 4 and 6?
This rule fails for non-co-prime numbers because they share common factors other than 1. For example, 4 and 6 share a common factor of 2. When you check divisibility for a number like 12, it is divisible by both 4 and 6. However, the product of 4 and 6 is 24. The rule doesn't hold because the shared factor (2) gets counted in both numbers, leading to an incorrect conclusion. For co-primes (like 3 and 4), there are no shared factors, so their product (12) correctly determines the divisibility test.
8. Beyond finding factors, what is the practical importance of the prime factorisation method taught in Class 6 Maths Chapter 3?
Prime factorisation is a fundamental concept in number theory with several important applications taught in Chapter 3 and beyond:
It is the most reliable method for finding the HCF and LCM of numbers.
It helps in simplifying fractions to their lowest terms.
It is a foundational skill for understanding more advanced topics in later classes, such as square roots, cube roots, and algebra. You can review the key formulas in Playing with Numbers Formulas for CBSE Class 6 Maths.
9. Where can I get reliable and updated NCERT Solutions for Class 6 Maths for the 2025-26 academic year?
You can find comprehensive and accurate NCERT Solutions for Class 6 Maths Updated for 2025-26 on Vedantu. These solutions are prepared by subject matter experts and provide step-by-step explanations for all exercises in Chapter 3, Playing with Numbers, and other chapters, strictly following the latest CBSE syllabus. You can also access NCERT Solutions for Class 6 All Subjects to support your overall learning.
