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# NCERT Solutions for Class 6 Maths Chapter 3: Playing with Numbers - Exercise 3.6

Last updated date: 09th Aug 2024
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## NCERT Solutions for Class 6 Maths Chapter 3 (Ex 3.6)

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 can be downloaded from the official Vedantu website. All the exercises and solutions are prepared by the expert teachers at Vedantu who have extensive experience of teaching this class. These NCERT Solutions are prepared in a step by step method to make it clear and understandable. The questions they have prepared will help the students ace the exam. The extensive practice will make sure that the students go to the exam with confidence. Subjects like Science, Maths, English,Hindi will become easy to study if you have access to NCERT Solution for Class 6 Science, Maths solutions and solutions of other subjects. You can also download NCERT Solutions for Class 6 Maths to help you to revise complete syllabus and score more marks in your examinations.

 Class: NCERT Solutions for Class 6 Subject: Class 6 Maths Chapter Name: Chapter 3 - Playing with Numbers Exercise: Exercise - 3.6 Content-Type: Text, Videos, Images and PDF Format Academic Year: 2024-25 Medium: English and Hindi Available Materials: Chapter WiseExercise Wise Other Materials Important QuestionsRevision Notes

## Access NCERT Solutions for Class 6 Maths Chapter 3 – Playing with Numbers

Exercise 3.6

Refer to page 19 for Exercise 3.6 in the PDF

1. Find the H.C.F of the following numbers:

(a) \[18,48\]

Ans: Prime factorization of  \[18\] is:

(Image Will Be Updated Soon)

Prime factorizationof \[48\] is:

(Image Will Be Updated Soon)

Thus,

The common factors between \[18\] and  \[48\] are \[2\] and \[3\]

. Thus ,H.C.F is 6.

(b) \[30,42\]

Ans: Prime factorization of \[30\] is:

(Image Will Be Updated Soon)

Prime factorization of \[42\] is:

(Image Will Be Updated Soon)

Thus,

The common factors between \[30\] and \[42\] are \[2\] and \[3\]

. Thus ,H.C.F is 6.

(c) \[18,60\]

Ans: Prime factorization of \[18\] is:

(Image Will Be Updated Soon)

Prime factorization of \[60\] is:

(Image Will Be Updated Soon)

Thus,

The common factors between \[18\] and \[60\] are \[2\] and \[3\]. Thus ,H.C.F is 6.

(d) \[27,63\]

Ans: Prime factorization of \[27\] is:

(Image Will Be Updated Soon)

Prime factorization of \[63\] is:

(Image Will Be Updated Soon)

Thus,

The common factor between \[27\] and \[63\] is \[3\] (2 times). Thus ,H.C.F is 9.

(e) \[36,84\]

Ans: Prime factorization of \[36\] is:

(Image Will Be Updated Soon)

Prime factorization of \[84\] is:

(Image Will Be Updated Soon)

Thus,

The common factors between \[36\] and \[84\] are  \[2\] (2 times) and \[3\]

. Thus ,H.C.F is 12.

(f) \[34,102\]

Ans: Prime factorization of \[34\] is:

(Image Will Be Updated Soon)

Prime factorization of \[102\] is:

(Image Will Be Updated Soon)

Thus,

The common factors between \[34\] and \[102\] are \[2\] and \[17\] . Thus ,H.C.F is 34.

(g) \[70,105,175\]

Ans: Prime factorization of \[70\]  is:

(Image Will Be Updated Soon)

Prime factorization of \[105\]  is:

(Image Will Be Updated Soon)

Prime factorization of  \[175\]  is:

(Image Will Be Updated Soon)

Thus,

The common factors between \[70\] , \[105\]  and \[175\] are \[5\]  and \[7\]

. Thus, H.C.F is 35.

(h) \[91,112,49\]

Ans: Prime factorization of \[91\]  is:

(Image Will Be Updated Soon)

Prime factorization of \[112\] is:

(Image Will Be Updated Soon)

Prime factorization of \[49\]  is:

(Image Will Be Updated Soon)

Thus,

The common factor between \[91\] , \[112\] and \[49\]  is \[7\]. Thus, H.C.F is \[7\].

(i) \[18,54,81\]

Ans: Prime factorization of \[18\] is:

(Image Will Be Updated Soon)

Prime factorization of  \[54\]  is:

(Image Will Be Updated Soon)

Prime factorization of  \[81\]  is:

(Image Will Be Updated Soon)

Thus,

The common factor between \[18\], \[54\]  and \[81\] is \[3\] (2 times). Thus, H.C.F is 9.

(h) \[12,45,75\]

Ans: Prime factorization of \[12\] is:

(Image Will Be Updated Soon)

Prime factorization of \[45\] is:

(Image Will Be Updated Soon)

Prime factorization of \[75\] is:

(Image Will Be Updated Soon)

Thus,

The common factor between\[12\], \[45\]  and \[75\]  is \[3\]. Thus, H.C.F is \[3\].

2. What is the H.C.F of two consecutive:

(a) numbers?

Ans: Out of two consecutive numbers, one will be an even number and other number will be an odd number, common factor between which is \[1\] only. Thus, H.C.F of two consecutive numbers is \[1\].

(b) even numbers?

Ans: Let the first even number be ‘x’ times, i.e., \[2x\] \[= 2(x)\], then second consecutive even number will be \[2x + 2 = 2(x + 1)\] One can observe that \[1\] and 2 are the common factors between \[2x\] and \[2x + 2\], and \[2\] is the highest value. Thus, H.C.F of two consecutive even numbers is 2.

(c) odd numbers?

Ans: Let the first odd number be \[2x + 1\] , then second consecutive odd number will be \[2x + 1 + 2 = 2x + 3\] One can observe that \[1\] is the common factor between \[2x + 1\] and  \[2x + 3\].Thus, H.C.F of two consecutive odd numbers is \[1\].

3. The H.C.F of co-prime numbers \[4\] and \[15\]was found as follows by factorization: and since there is no common prime factor, so H.C.F of \[4\] and \[15\]is 0 . Is this answer correct? If not, what is the correct H.C.F?

Ans: The H.C.F of co-prime numbers pair is \[1\] Because \[4\] and \[15\]are co-prime numbers, therefore H.C.F of \[4\] and \[15\] is \[1\].

Thus, \[0\] is not the H.C.F of \[4\] and \[15\]but \[1\]  is the H.C.F of \[4\] and \[15\]’.

## Chapter 3: Playing with Numbers

The following are the subtopics given in the chapter.

• Exercise 3.1 Introduction

• Exercise 3.2 Factors and Multiples

• Exercise 3.3 Prime and Composite Number

• Exercise 3.4 Tests for Divisibility of Numbers

• Exercise 3.5 Common Factors and Common Multiples

• Exercise 3.6 Some More Divisibility Rules

• Exercise 3.7 Prime Factorization

• Exercise 3.8 Highest Common Factor

• Exercise 3.9 Lowest Common Multiple

• Exercise 3.10 Some problems of HCF and LCM

The following is a thorough detail of what the students are required to cover in each section and how Vedantu will help them out.

### 3.1 Introduction

Numbers are the foundation of mathematics. Numbers are what math began with. This chapter ‘plays with numbers’ and explores the different properties of numbers such as prime numbers, composite numbers, factors and multiples, HCF, LCM, etc.

The first section of this chapter briefly details what will be covered in it. The students are introduced to using multiplication instead of addition in counting larger blocks of items quickly.

They will also learn about factors and multiples. The students have already mastered multiplication and division in the previous classes. In this class, they will learn how they can use previous knowledge for new types of concepts.

This section forms the basis of the entire chapter. It addresses the simple concepts and properties of numbers. For example, students will learn that any number is a multiple of itself. They will explore this concept in detail. Instead of just memorizing it, they will learn why it is so.

Vedantu facilitates this through the practise questions given in the pdf. The students can attempt the practice questions themselves first. Then, they can see the solution for exercise 3.6 class 6 and see if their answers were correct.

Another concept the students explore is that every multiple of a number is greater than or equal to the number itself. Such information may seem like common sense to us. However, at this stage, it is essential to explain it to the students.

Explaining these concepts will help to integrate them as part of the students’ common sense.

### 3.2 Factors and Multiples

In this section, students learn details about factors and multiples. They will learn to differentiate between the two terms.

Often, students get confused between the two when they are solving questions later in the chapter.

Vedantu makes sure to offer good practice so that students don’t confuse the two concepts. They will learn about the basic properties of factors and multiples. For example, they will learn that the number of factors of a given number is finite. However, the number of multiples of a given number is infinite.

### 3.3 Prime and Composite Number

This section begins with defining prime and composite numbers. A prime number is a number that is divisible by one and itself only. In this section, students will be given true and false questions. For example, is 4 a prime number? They will also be asked to explain the reason as to why 4 is not a prime number. If they have given the incorrect answer to this question, they can refer to the solutions of the exercises. A teacher can help them understand why their reasoning was incorrect. There are many questions for practice in class 6 maths chapter 3 exercise 3.6 that addresses all the types of questions where students commonly make mistakes.

Furthermore, Vedantu encourages students to explore the topic and learn tips and tricks about it. For example, a tip that students can derive by solving the exercise is that even numbers can never be prime. This is because all even numbers are divisible by 2. Also, numbers that are multiples of other digits can never be prime numbers.

By exploring such aspects about prime numbers, students will get a stronger grip on the topic.

This topic serves to form the basis for future topics such as factorization that the students will learn later.

Another type of exercise in class 6 maths ch 3 ex 3.6 of this section is that students will be given an array of numbers. They will be asked to count all of the prime numbers and then decide whether the sum is prime or composite. Such activities are not only fun for the students, but they also help to drill the concept in the students’ minds.

### 3.4 Tests for Divisibility of Numbers

The students had mastered all their tables, multiplication and division by Class 5. They know how to use long division and three-digit multiplication. In NCERT Solutions for Class 6 maths exercise 3.6, they will learn simple tips and tricks about multiplication and division. This section builds on previous knowledge that the students have learned from the previous classes.

By learning simple divisibility rules, the students will be able to tell with one glance that a number is divisible by another or not. Students will learn the rules for numbers 2, 3, 4, 5, 6, 7, 8, 9, and 10.

First, the students are asked to apply the divisibility rule given in their textbooks to the NCERT Solution Class 6 maths chapter 3 exercise 3.6. Then they will manually check their answer by dividing the numbers. This will help the students to revise their multiplication and division skills and also drill the rules.

Once the students have mastered all the divisibility rules, they will begin to see patterns in them. As they solve the class 6 maths exercise 3.6, they will understand the reasons behind the rules. This will help them derive more tips and tricks. Also, they will become familiar with the art of reasoning. This comes in handy when students begin to learn Geometry in later classes.

Furthermore, learning these divisibility rules has many practical applications in daily life. For example, if a student wants to split eight toffees among three friends, he will know that it is not possible.

So, divisibility rules also form the basis of learning percentages and fractions later in the course.

Vedantu makes sure that the students get ample practice of each concept and don’t make any of the common errors while solving the exercise.

### 3.5 Common Factors and Common Multiples

In section 3.5 of the chapter, students are introduced to the concepts about common factors and common multiples. First, they are taught how to differentiate between factors and multiples. Vedantu does this by giving multiple-choice questions and True & False type questions in the exercise. The students are asked to differentiate between factors and multiples in a given question. They can use the NCERT Solution for class 6 maths chapter 3 exercise 3.6 to recheck their answers.

Then the students will be asked to write down the multiplication tables of that number and carefully identify the common factors and common multiples. For example, 1, 2, 3, and 6 are common factors of 6. 0, 6 and 12 are multiples of 6.

A common mistake that students make is to confuse between 0 and 1. Vedantu addresses this issue by giving multiple-choice questions on this topic. Vedantu gives a rigorous drill that makes sure that students do not forget any important concept in the exam. Some of the questions in Vedantu’s exercises are from past papers. This helps the students understand what type of questions will be tested in the exam. It also encourages the students that the question they are doing could come in their exams.

After students have learned the basics of the common multiples and factors, they won’t need to write all the tables of the numbers. They can simply use the factorization method to solve the question. They can then check their answers on the class 6 maths NCERT Solutions ex 3.6.

### 3.6 Some More Divisibility Rules

In this section, the students will earn some more divisibility rules. This section builds on section 3.4. For example, students will learn rules that if a number is divisible by another number, it means that it is divisible by each of the factors of that number. This helps the students in understanding all aspects of the divisibility rules.

In this section, the concept of a prime number is revisited. The students will use the definition of prime numbers to use another rule. If a number is divisible by two co-prime numbers, it means that the number is also divisible by the product of both the numbers. This rule isn’t difficult to understand for most students. It offers insights as to how students can derive a rule on the basis of information.

Another rule introduced in this section is that if two numbers are divisible by a number, it means that their sum is also divisible by that number. This rule may sound intuitive to us, but it is not so for students of Class 6.

Vedantu helps to develop the students reasoning and understanding of such concepts. This helps to expand students' reasoning skills as well.

Vedantu has designed different types of exercises to address all aspects of such questions. For example, in on exercise, Vedantu asks the students to identify which rule as applied in a given question. This helps to form the basis for Algebra and Geometry proofs that the students will learn in future classes.

### 3.7 Prime Factorization

In section 3.7 of NCERT Solutions for class 6 maths chapter 3 exercise 3.6, students learn the concept of factorization using prime numbers. They will apply all the previously learned concepts in this section.

Vedantu gives an all-rounded practice in this section. As the students will solve the new exercises, Vedantu makes sure that they are revising the previous concepts as well. This helps the students to make their practice error-free before the exam.

For example, in the prime factorization of 36, the students will apply their knowledge of prime numbers and divisibility rules. First, they will determine all the factors of 36. Then, they will find the factors of those factors and determine which ones are prime. The exercises in the Vedantu PDF requires you to show all the steps and thought processes required for the question.

The concept of making a factor tree is also introduced here. This will help the students when they have to do factorization with variables in Class 7 Algebra.

The Vedantu PDF follows the pattern and steps of the NCERTs Maths textbook. This makes sure that all the questions are according to the level of the students, and none of the questions is beyond the scope of the syllabus.

Vedantu offers an extensive practice that is exactly in accordance with the syllabus and exam pattern. This will help students, parents and teachers alike so that they don’t have to look for practice material from other sources.

### 3.8 Highest Common Factor

Section 3.8 introduces the concept of the Greatest or Highest Common Factor (GCF or HCF.) The students use their knowledge of factorization and divisibility rules to find the greatest common multiple.

Vedantu offers a number of exercise questions so that students get ample practice of the concept. Students tend to make a lot of mistakes in this section. The questions will make sure that the students eliminate common errors before the exam. Many questions from Vedantu show up in the exams, so these practice questions are just like a mock exam.

Furthermore, these practice questions are exactly in accordance with the paper pattern. None of the questions is out of syllabus. So, the students are required to solve all of them and show all the steps. Showing all the steps helps to identify exactly where the error occurred. Usually, when students get an answer wrong, they think that they are ‘bad’ at the subject. Vedantu makes sure that the students don’t fall into this trap due to minor issues that can be fixed.

In this section, Vedantu has also added questions that require theorization and application of knowledge rather than a simple application of traditional steps. For example, a common question is to determine the highest common divisor of two consecutive odd numbers. This question is different from what students have done previously. It requires higher-level thinking and extensive reasoning. Such questions also strengthen the students’ grasp of the concepts. They make sure that they understand the definition inside out.

Another type of question is that the GCF of the numbers is given and the students are asked to guess what the numbers were. Such a question that requires the reverse steps also helps to drill the concept in the students’ minds.

If the students are not sure about how to approach a question, they can view the tips or solved examples. Once they get a head-start, they can solve the question easily.

### 3.9 Lowest Common Multiple

This section addresses the LCM or Lowest Common Multiple of two numbers. Vedantu has given a series of exercises to apply this concept. The textbook has given clearly defined steps to approach this question. Vedantu makes sure that the students use the same steps to arrive at the answer.

This section requires that students have mastered the concepts of prime numbers and factorization thoroughly. If the students are not good at those topics, they will struggle with these questions as well. Also, this section gives further practise of those topics as well.

Vedantu has designed different types of questions for this topic. There are some multiple-choice questions that only require the students to state the answer without showing all the steps. There are also true and false questions in the exercises. Vedantu has also made some subjective type questions that require all the steps in detail.

Vedantu has also given interesting questions at the end of this section. In these questions, numbers are given and the students have to find the GCF, LCM, factors and multiples of numbers from that array of numbers. This is like a crossword puzzle that students have to solve. Students enjoy such questions as they can be creative and use different coloured pencils to fill in the answers.

Such activities let the students enjoy maths. Usually, students perceive mathematics as a difficult and dry subject. Vedantu aims to change this perception. At Vedantu, Math is not only made easy for the students, but it is also made more fun and engaging.

### 3.10 Some problems of HCF and LCM

This is the most important section of this chapter. It gives practical situations that require the students to apply all the concepts they have learned in the chapter.

Vedantu makes sure that the exercises in this section are relevant to the students’ daily life. Many times, kids complain that they don’t actually use math in their daily life, so what’s the point of learning it? This section answers that question as well.

For example, a question given in the Vedantu PDF is that if you buy two bags of fertilizer of weights 75 kg and 69 kg, then find the maximum value of weight which can measure the fertilizer. This kind of problem is faced every day. Students will learn to apply their theoretical knowledge to it.

Another type of question is to find two sets of numbers that have the same LCM. For this question, the students have to apply divisibility rules and eliminate the options that are not possible. Then, they will proceed to find the LCM of the options that are still left. By attempting such types of questions, students will learn how they should approach the exam questions and save time on doing extra steps that are not needed.

Also, this section introduces the students to find the LCM and GCF of more than two numbers.

Such a thorough practice ensures that the students will master the skills perfectly. Such questions also make sure that the students are confident when they go for the exam.

With Vedantu, you don’t have to hunt for guides to review for the exam as you will find everything in one place. It offers a systematic and thorough revision of each concept.

It also offers the facility for easy downloading. Many other platforms demand payments before you can start using their services. With Vedantu, everything is free and available at your fingertips.

If a student needs help, experienced teachers at Vedantu will be there to guide them. Vedantu helps the students learn how to self-study. Students are required to solve all the practice questions themselves and then check them as well. When the students compare their solutions to the ones given in the Vedantu PDF and check them, they learn how the examiners check their exam papers. This helps them learn how to attempt the paper better.

With Vedantu, students will achieve the success that feels only like a dream to others.

### Why Vedantu?

Vedantu uses technology to help students prepare for their exams. In a world where technology and IT are taking over every sphere of life, it is important that the ways of studying be revolutionized as well.

This not only makes studying easier, but it also helps in studying at home. Students don’t have to join academies when they have Vedantu. Whether its midnight or early morning, the students can prepare for the exam whenever they need to. This way, they don’t get bound to academies to get good grades.

Many parents don’t like academies because of the rote learning they teach the students. Vedantu makes sure that the students are not simply memorizing the information. The teachers at Vedantu have designed the questions in a way to make sure that there are all types of questions: factual, application and theorizing questions. This aids the students in assessing their knowledge thoroughly.

Furthermore, Vedantu is very popular with students who can’t afford expensive tutors and academies. Vedantu provides good quality education to everyone. Imagine that all of this is free!

Vedantu has also made education cheaper and more accessible to everyone. This way the effects of high-quality education will be far-ranging.

Vedantu is popular for many of its features that are designed to help the students in acing their exam with flying colours.

Whenever a student gets stuck, he or she can request help from expert teachers. The teacher will conduct an audio or video session to address all the queries the students may have.

Moreover, you do not need a high-speed net to download from Vedantu. It works on a low-speed Internet as well. The documents are in pdf format which makes them easier to download. Within seconds, you will have the chapter guide you need. Vedantu extends its services to places where the Internet connection is not good. This way, no student will be deprived of quality education.

With Vedantu, you don’t have to run after teachers to give you helping material. All the material you will ever need to study effectively is available on a single platform.

Also, you have many teachers available to help you. So, if you don’t understand the way a teacher explains, you can always consult another teacher. Vedantu works to remove all the barriers that occur in spreading education.

Vedantu also replicates the traditional classroom settings in its online teaching methodologies. So, it is an online classroom with a traditional touch. As the teacher writes on the whiteboard, students can view it in real-time. The best teaching method is known to be when the teacher delivers the lecture on the whiteboard and the students can stop the teacher whenever they have a query or don’t understand a concept. At Vedantu, the teacher writes on the whiteboard while the students are on the live video call. They can ask the teacher anything they want in real-time without having to wait for a question and answer session.

So, Vedantu makes sure that there are no drawbacks of studying online and has solutions to turn the disadvantages into advantages.

Students and teachers can also share pictures and textbooks with each other. Before the live session begins, the teacher can upload helping material on the shared whiteboard. The students can download the documents and view them before the online session begins.

In a traditional classroom, you cannot playback a lecture. All you can do is try to quickly take notes in the lecture. Most teachers don’t allow mobile phones in the classroom to record the lecture. So, you can take the lecture only once.

At Vedantu, there is a solution to this too. You can easily playback the live session later on. This comes in handy for students in case they couldn’t make it to the live session. The replay of the live session can help the students in clarifying their concepts. The live session recording also helps when the students want to quickly revise the topic for an exam. They can play the recording anywhere they want.

The question and answers guides provide model answers written by experienced teachers. These guides, textbooks, and live sessions are the perfect formula for students’ success in the exam. Such a step-by-step thorough revision also gives the students the confidence they need to ace the exam.

The sheer number of students who have benefited from Vedantu is proof that this platform can make radical changes in educating students. Education is the country’s future and Vedantu is helping the country as well as the students in excelling.

So, what are you waiting for?

You don’t need to pay a penny. Just make sure that you do all the exercises the way Vedantu asks you, and no one will be able to stop you from achieving your success.

## FAQs on NCERT Solutions for Class 6 Maths Chapter 3: Playing with Numbers - Exercise 3.6

1. Does Vedantu provide answers to all the questions of Exercise 3.6 of Chapter 3 of Class 6 Maths?

Exercise 3.6 of "Playing with Numbers" contains three questions in total. You will find the solutions to all the three questions on Vedantu's NCERT Solutions for Exercise 3.6 of Chapter 3 of Class 6 Maths. No question is left unanswered by Vedantu.

The solutions are explained step by step so that students can understand the correct way of forming the answers.  You will be easily able to understand the solutions as they are prepared by genuinely talented teachers to suit the intellect level of Class 6 students.

2. What concept should I study well to excel in Exercise 3.6 of Chapter 3 of Class 6 Maths?

The three questions of Class 6 Maths Exercise 3.6 are based on the concept of the Highest Common Factor or HCF. The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common Divisor (GCD).

HCF is a fairly simple concept to understand but an important one indeed. You will be using HCF for many things later on and hence you must comprehend his topic expertly.

3. Is Exercise 3.6 of Chapter 3 of Class 6 Maths easy?

Yes, Exercise 3.6 of "Playing with Numbers" is a pretty straightforward exercise asking you to find the Highest Common Factor of certain numbers.

The concept of HCF is very easy and you must practice it. In case you are unable to understand certain things about HCF, you can refer to Vedantu's NCERT Solutions for Exercise 3.6 of Chapter 3 of Class 6 Maths. As you scroll down below the solutions, you will find added explanations of the chapter to enhance your understanding.

4. How can I download the NCERT Solutions for Exercise 3.6 of Chapter 3 of Class 6 Maths?

To download the solutions in PDF format for Exercise 3.6 of Chapter 3 of Class 6 Maths:

1. Go to Vedantu's NCERT Solutions for Class 6 Maths and select Exercise 3.6.
2. Scroll down on the following page and click on the option to "Download PDF."
3. You will be promptly taken to a new page containing the link for automatic download of the required PDF.

If you have installed the Vedantu mobile app, you can easily download these solutions

from there as well.

The solutions are free of cost.

5. Suggest a study plan to effectively study Class 6 Maths Chapter 3 “Playing with Numbers.”

Class 6 Chapter 3 "Playing with Numbers" is a long chapter containing seven exercises in total. Although the chapter is long, the concepts taught in it are fairly uncomplicated. To meticulously study this chapter:

1. Read the NCERT textbook well. Refer to Vedantu's explanations for an added understanding of the chapter.
2. Try to solve the questions of this chapter yourself then refer to Vedantu's Solutions for self-assessment.
3. Practice all the questions and examples multiple times to champion the content of the chapter.