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NCERT Solutions for Class 6 Maths Chapter 3: Playing with Numbers - Exercise 3.3

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NCERT Solutions for Class 6 Maths Chapter 3 (Ex 3.3)

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3 provided by Vedantu is as per the latest syllabus of CBSE Class 6 Mathematics. Playing with Numbers Class 6 Exercise 3.3 Solution brings a step by step guide to preparing for exams as per the NCERT books for Class 6 Maths. Compliment exam practice with our Class 6 Maths NCERT Solutions Chapter 3 Exercise 3.3 available online. Students can download NCERT Solutions to have an edge during exams.


Class:

NCERT Solutions for Class 6

Subject:

Class 6 Maths

Chapter Name:

Chapter 3 - Playing with Numbers

Exercise:

Exercise - 3.3

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes



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.

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

Exercise 3.3

1. Using the divisibility test, determine which of the following numbers are divisible by \[\mathrm{2}\]; by \[\mathrm{3}\]; by \[\mathrm{4}\]; by \[\mathrm{5}\]; by \[\mathrm{6}\]; by \[\mathrm{8}\]; by \[\mathrm{9}\]; by \[\mathrm{10}\] ; by \[\mathrm{11}\]. (Say yes or no).

Number

Divisible by 


\[\mathrm{2}\]

\[\mathrm{3}\]

\[\mathrm{4}\]

\[\mathrm{5}\]

\[\mathrm{6}\]

\[\mathrm{8}\]

\[\mathrm{9}\]

\[\mathrm{10}\]

\[\mathrm{11}\]

\[\mathrm{128}\]

Yes

No

Yes

No

No

Yes

No

No

No

\[\mathrm{990}\]










\[\mathrm{1586}\]










\[\mathrm{275}\]










\[\mathrm{6686}\]










\[\mathrm{639210}\]










\[\mathrm{429714}\]










\[\mathrm{2856}\]










\[\mathrm{3060}\]










\[\mathrm{406839}\]










Ans:

Number

Divisible by 


\[\mathrm{2}\]

\[\mathrm{3}\]

\[\mathrm{4}\]

\[\mathrm{5}\]

\[\mathrm{6}\]

\[\mathrm{8}\]

\[\mathrm{9}\]

\[\mathrm{10}\]

\[\mathrm{11}\]

\[\mathrm{128}\]

Yes

No

Yes

No

No

Yes

No

No

No

\[\mathrm{990}\]

Yes

Yes

No

Yes

Yes

No

Yes

Yes

Yes

\[\mathrm{1586}\]

Yes

No

No

No

No

No

No

No

No

\[\mathrm{275}\]

No

No

No

Yes

No

No

No

No

Yes

\[\mathrm{6686}\]

Yes

No

No

No

No

No

No

No

No

\[\mathrm{639210}\]

Yes

Yes

No

Yes

Yes

No

No

Yes

Yes

\[\mathrm{429714}\]

Yes

Yes

No

No

Yes

No

Yes

No

No

\[\mathrm{2856}\]

Yes

Yes

Yes

No

Yes

Yes

No

No

No

\[\mathrm{3060}\]

Yes

Yes

Yes

Yes

Yes

No

Yes

Yes

No

\[\mathrm{406839}\]

No

Yes

No

No

No

No

No

No

No

2. Using the divisibility test, determine which of the following numbers are divisible by \[\mathrm{4}\]; by \[\mathrm{8}\].

(a) \[\mathrm{572}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Not divisible by \[\text{8}\] as its last three digits are not divisible by \[\text{8}\].

(b) \[\mathrm{726352}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Divisible by \[\text{8}\] as its last three digits are divisible by \[\text{8}\].

(c) \[\mathrm{5500}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Not divisible by \[\text{8}\] as its last three digits are not divisible by \[\text{8}\].

(d) \[\mathrm{6000}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Divisible by \[\text{8}\] as its last three digits are divisible by \[\text{8}\].

(e) \[\mathrm{12159}\]

Ans: Not divisible by \[\text{4}\] and \[\text{8}\] as it is an odd number.

(f) \[\mathrm{14560}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Divisible by \[\text{8}\] as its last three digits are divisible by \[\text{8}\].

(g) \[\mathrm{21084}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Not divisible by \[\text{8}\] as its last three digits are not divisible by \[\text{8}\].

(h) \[\mathrm{31795072}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Divisible by \[\text{8}\] as its last three digits are divisible by \[\text{8}\].

(i) \[\mathrm{1700}\]

Ans: Divisible by \[\text{4}\] as its last two digits are divisible by \[\text{4}\].

Not divisible by \[\text{8}\] as its last three digits are not divisible by \[\text{8}\].

(j) \[\mathrm{2150}\]

Ans: Not divisible by \[\text{4}\] as its last two digits are not divisible by \[\text{4}\].

Not divisible by \[\text{8}\] as its last three digits are not divisible by \[\text{8}\].

2. Using the divisibility test, determine which of the following numbers are divisible by \[\mathrm{6}\].

(a) \[\mathrm{297144}\]

Ans: Divisible by \[\text{2}\] as its units place is an even number.

Divisible by \[\text{3}\] as the sum of its digits \[\left( =27 \right)\] is divisible by \[3\].

Since the number is divisible by both \[2\] and \[3\], therefore it is also divisible by \[6\].

(b) \[\mathrm{1258}\]

Ans: Divisible by \[\text{2}\] as its units place is an even number.

Not divisible by \[\text{3}\] as the sum of its digits \[\left( =16 \right)\] is not divisible by \[3\].

Since the number is not divisible by both \[2\] and \[3\], therefore it is not divisible by \[6\].

(c) \[\mathrm{4335}\]

Ans: Not divisible by \[\text{2}\] as its units place is not an even number.

Divisible by \[\text{3}\] as the sum of its digits \[\left( =15 \right)\] is divisible by \[3\].

Since the number is not divisible by both \[2\] and \[3\], therefore it is not divisible by \[6\].

(d) \[\mathrm{61233}\]

Ans: Not divisible by \[\text{2}\] as its units place is not an even number.

Divisible by \[\text{3}\] as sum of its digits \[\left( =15 \right)\] is divisible by \[3\].

Since the number is not divisible by both \[2\] and \[3\], therefore it is not divisible by \[6\].

(e) \[\mathrm{901352}\]

Ans: It is divisible by \[\text{2}\] since its unit place is even number.
Sum of the digits of the given number is \[20\], which is not divisible by \[3\].

Here the number is not divisible by both \[2\] and \[3\], so it is not divisible by \[6\].

(f) \[\mathrm{438750}\]

Ans: It is divisible by \[\text{2}\] since its unit place is even number.
Sum of the digits of the given number is \[27\], which is divisible by \[3\].

Here the number is divisible by both \[2\] and \[3\], so it is divisible by \[6\].

(g) \[\mathrm{1790184}\]

Ans: It is divisible by \[\text{2}\] since its unit place is even number.
Sum of the digits of the given number is \[30\], which is divisible by \[3\].

Here the number is divisible by both \[2\] and \[3\], so it is divisible by \[6\].

(h) \[\mathrm{12583}\]

Ans: It is not divisible by \[\text{2}\] since its unit place is not an even number.
Here the number is not divisible by both \[2\] and \[3\], so it is not divisible by \[6\].

(i) \[\mathrm{639210}\]

Ans: It is divisible by \[\text{2}\] since its unit place is even number.
Sum of the digits of the given number is \[21\], which is divisible by \[3\].

Here the number is divisible by both \[2\] and \[3\], so it is divisible by \[6\].

(j) \[\mathrm{17850}\]

Ans: It is divisible by \[\text{2}\] since its unit place is even number.
Sum of the digits of the given number is \[23\], which is not divisible by \[3\].

Here the number is not divisible by both \[2\] and \[3\], so it is not divisible by \[6\].

3. Using the divisibility test, determine which of the following numbers are divisible by \[\mathrm{11}\].

(a) \[\mathrm{5445}\]

Ans:

Odd places sum\[\text{=4+5=9}\]

Even places sum \[\text{=4+5=9}\]

Difference \[\text{=9-9}\]

Though the difference is \[0\], the number is divisible by \[11\].

(b) \[\mathrm{10824}\]

Ans:

Odd places sum\[\text{=1+8+4=13}\]

Even places sum \[\text{=0+2=2}\]

Difference \[\text{=13-2=11}\]

Though the difference is \[11\], the number is divisible by \[11\].

(c) \[\mathrm{7138965}\]

Ans: Odd places sum\[\text{=7+3+9+5=24}\]

Even places sum \[\text{=6+8+1=15}\]

Difference \[\text{=24-15=9}\]

Though the difference is \[9\], the number is not divisible by \[11\].

(d) \[\mathrm{700169308}\]

Ans: Odd places sum\[\text{=8+3+6+0=17}\]

Even places sum \[\text{=6+8+1=15}\]

Difference \[\text{=17-15=2}\]

Though the difference is \[2\], the number is not divisible by \[11\].

(e) \[\mathrm{10000001}\]

Ans: Odd places sum\[\text{=1+0+0+0=1}\]

Even places sum \[\text{=0+0+0+1=1}\]

Difference \[\text{=1-1=0}\]

Though the difference is \[0\], the number is divisible by \[11\].

(f) \[\mathrm{901153}\]

Ans: Odd places sum\[\text{=9+1+5=15}\]

Even places sum \[\text{=3+1+0=4}\]

Difference \[\text{=15-4=11}\]

Though the difference is \[11\], the number is divisible by \[11\].

4. Write the smallest digit and the largest digit in the blanks space of each of the following numbers so that the number formed is divisible by \[\mathrm{3}\].

(a) \[........\mathrm{6724}\]

Ans: To get divisible by \[\text{3}\] the sum of the digits should be divisible by \[\text{3}\].

So, the sum of the digits of the given number is \[\text{6+7+2+4=19}\].

So, the least digit will be \[\text{2 }\left( 19+2=21 \right)\] and largest digit will be \[8\text{ }\left( 19+8=27 \right)\].

(b) \[\mathrm{4765 }\!\!\_\!\!\text{ 2}\]

Ans: To get divisible by \[\text{3}\] the sum of the digits should be divisible by \[\text{3}\].

So, the sum of the digits of the given number is \[\text{4+7+6+5+2=24}\].

So, the least digit will be \[\text{0 }\left( 24 \right)\] and the largest digit will be \[\text{9 }\left( 24+9=33 \right)\].

5. Write the smallest digit and the largest digit in the blanks space of each of the following numbers so that the number formed is divisible by \[\mathrm{11}\].

(a) \[\mathrm{92 }\!\!\_\!\!\text{ 389}\]

Ans: To get divisible by \[11\] ,the difference between the sum of digits in odd places and even places should be \[0\] or \[11\].

Odd places: \[9+8+8=25\]

Even places: \[2+3+9=14\]

Difference: \[25-14=11\]

Therefore \[8\] is the largest and smallest digit.

(b) \[\mathrm{8 }\!\!\_\!\!\text{ 9484}\]

Ans: To get divisible by \[11\] ,the difference between the sum of digits in odd places and even places should be \[0\] or \[11\].

Odd places: \[8+9+8=25\]

Even places: \[6+4+4=14\]

Difference: \[25-14=11\]

Therefore \[6\] is the largest and smallest digit.

Class 6 Maths NCERT Solutions Chapter 3 Exercise 3.3 – An overview

The chapter Playing with Numbers introduces students to divisions of different numbers. The entire NCERT Class 6 Maths Chapter 3 is about learning various concepts of Mathematics and applying them to solve the given sums. These exercises help to boost the analysing ability of students early on in their curriculum.

This chapter gives an in-depth explanation of the concepts listed down below. 

  • Factors and Multiplications.

  • Prime and Composite Numbers.

  • Test for Divisibility of Numbers.

  • Common Factors and Common Multiples.

  • Other Divisibility Rules.

  • Prime Factorisation.

  • Highest Common Factor.

  • Lowest Common Multiple.

  • Problems on H.C.F. and L.C.M.

Now, coming to Chapter 3 Maths Class 6 Exercise 3.3, almost all questions in this exercise deal with the various methods of divisibility of even numbers and odd numbers. These exercises will allow students to master the different techniques that can further help enhance their mental ability.

After a quick study through the PDF version of our NCERT Maths book Class 6 Chapter 3 Solutions, students can become ready beforehand to solve such tricky divisibility tests. The study material provided in our Class 6th Maths Chapter 3 Exercise 3.3 is according to the latest CBSE syllabus and includes multiple shortcut techniques to prepare for the upcoming exams with ease.

Our subject experts have poured their insights to prepare a handy guide that can help students acquire excellence in solving sums related to Playing with Numbers. 


Playing with Numbers Exercise 3.3 – All Questions

This particular chapter comprises of six questions. The pattern differs for each question as per the three segments. Among this exercise – 

  • The very first question is within a chart. It asks whether some numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10 and 11. A student has to answer whether a number is divided by the asked fraction or not.

  • The second, third and fourth questions ask whether a few numbers are divisible by 4 and 8, 6 and 11 respectively.

  • In the last two questions, the question type is filling in blanks. Students thus have to find the correct answer as per the chapter’s concepts and fill in to make the given sentence meaningful and justified. 

Our subject experts with years of experience behind them have compiled our NCERT Maths Class 6 Chapter 3 Exercise 3.3 for better exam preparation. Thus, for thorough revision, a student can use our guide, which follows the latest syllabus module notified by NCERT. Following questions are explained in our NCERT Class 6 Maths Chapter 3 – 

A. Class 6 Maths Chapter 3 Exercise 3.3 – Question 1

The very first question is a divisibility test. It asks you to determine whether a few numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10 and 11. 

If the numbers are divisible by the series of numbers given, students need to answer it in “yes” and if it doesn’t, then in “no”. 

This chapter is based primarily on the concept of Prime numbers and Composite numbers. As per this concept, for a number other than 1 is divisible only by 1, then it is called a ‘Prime Number’. Example of prime numbers is 2, 3, 5, 7 and 11. Similarly, students can go on finding prime numbers in the number series by checking their divisibility.

Next, students will also learn that a number which has more than two factors; it is called a ‘Composite Number’. Example of composite numbers is 4, 6, 8, 10 and so on.

The question is given in a chart. A student has to calculate the answer and confirm its divisibility. As the figures are quite high, its calculation can be done on a rough sheet. Further, students can access the Playing with Numbers solution to learn shortcut techniques for finding the right answer. 

As incorporating a chart within a question makes even the easiest question tricky, complementing your learning with our online solutions can simplify the experience. To answer the questions more efficiently, a student can go through other exercises within Chapter 3 Playing with Numbers. 

A brief introduction of different concepts of Mathematics is given from the 1st exercise of Chapter 3.  In this chapter, a student thus gets to learn mainly about multiplication and division.

As for the first question of Exercise 1, it teaches students to figure out the factors of given figures. They can thus carry on this learning to efficiently solve the questions in Exercise 3.3. It is a quick trick to sharpen a student’s ability to find the primary and composite numbers from the list only through divisibility method.

The second question is about calculating the initial five multiples of the given figures, and the next question can be a brain teaser during an examination. A student has to match the figures on the left column with factors given in the right column. The last question of Exercise 3.1 is about figuring out the multiples from 9 to 100.

An overview of the other exercises from the same chapter helps a student to understand different methods used in a specific chapter and practise accordingly for better exam preparation. 

Not only this, but an overview also prepares a student to easily understand complicated approaches in Mathematics, which equips them for the subject in higher classes.

These techniques of Mathematics are not only applicable to students studying in the sixth standard. But, learning these methodologies would also help a student in his/her higher studies. Each exercise of this chapter focuses on nurturing a student’s mind and preparing them to develop necessary problem-solving skills.  

A student can go through our CBSE book solutions and understand the different concepts of maths mentioned in this chapter Playing with Numbers. The study material gives a clear idea about the question pattern and approach behind every question, thus enabling students to solve them efficiently.

After having a thorough reading of our solution to Playing with Numbers Class 6, a student can easily prepare for their exams. In the PDF version of the study material, a detailed description of Prime Numbers and Composite Numbers is given. Plus, an ample number of examples for such tricky questions ease the process of learning. Other than the examples, students can also try their hands at various exercises for practice. It helps students maintain a lucid approach towards the answers derived from related mathematical concepts for each exercise.

B. NCERT Solution for Class 6 Maths Chapter 3 exercise 3.3 – Question 2

In this question, students have to figure out if the given numbers are divisible by 4 and 8 or not. Before answering the questions, students must learn about two important short-cut method of facing such problems of Mathematics.

  • Determining the divisible figures of four - To determine whether a three or four-digit number can be divided by 4, a student can try to divide the last two digits by four. For example, figure 424 is divisible by 4 because the last two digits are divisible by 4.

  • Determining the divisible figures of eight - In the case of number 8, a student can divide the last three digits of a four or five-digit figure. If the last three digits are divisible by eight, then the total figure is easily divisible by eight. For example, figure 2840 can be divided by 8 because the last three digits of the figure are divisible by 8.

Now, coming back to the problems asked in Playing with Numbers Class 6 Exercise 3, there are eight sub-sections. In each question, a student has to figure out if the numbers are divisible by either four or eight. 

These questions are set in a way that allows a student to divide every figure twice by both 4 and 8. With the above-stated method, a student can quickly calculate and solve the sums accurately. A student can learn various other techniques in this specific chapter of Playing with Numbers by going through the NCERT solutions provided by Vedantu for free. 

To get a better idea about the concepts taught in this specific chapter, a student can have a quick look at the other exercise within the chapter. For example, the 2nd exercise comprises various concepts related to prime numbers and composite numbers. By practising this exercise, a student can also have an insight into the concept of odd numbers and even numbers.

The second exercise covers around twelve questions which are all short in length. The first of these asks the summation of odd numbers and even numbers.

Within this list, the second question is about stating whether the statements are true or false spread over ten sub-sections. A student has to determine which one is correct and which one isn’t as per his/her learning.

The next three questions are about determining prime numbers. Students can easily identify each prime number and write their answers with confidence with a thorough practice aided by NCERT Solution for Playing with Numbers.

Question 6, 8 and 10 are multiple-choice questions related to odd numbers and even numbers. And, question numbers 5, 7, 9 and 11 include a few sums related to prime numbers and composite numbers.

The last question in this list, i.e. the 12th question, is about filling the blanks. The concepts covered in these problems are an odd number, a prime number and composite number.

Having a proper understanding of other exercises in this chapter helps students solve Exercise 3.3 of Playing with Numbers with greater efficiency.

These exercises pave the way for developing a strong foundation in students regarding numbers. 

Plus, there are around six other chapters in the CBSE syllabus for Class 6 Mathematics. With a thorough practice from the beginning, the base for the next chapter will be strong.

With our online version of the solved question guide of Class 6 Exercise 3.3, a student can practise the various rules with the additional examples provided. These solutions help to score higher marks with ease.

C. NCERT Solution Class 6 Maths Chapter 3 Exercise 3.3 – Question 3

The next question in the list is almost the same as the previous question. In this section, there are ten sub-sections. Each of these sub-sections asks students to determine whether a number is divisible by 6 or not.

Another trick for solving such questions is to understand a simple method of calculation. To determine if a number is divisible by 6 or not, a student has only to figure out if that number is divisible by both 2 and 3. It helps determine the perfect factor for a given number.

For example, figure 42 is divisible by both 2 and 3. Hence, it’ll also be divided by 6. In case of a figure like 45, which is only divided by 3, it won’t be divided by 6. 

To simplify the process of learning, students can use easy tips for determining if a figure is divisible by two and three.

  • Tip 1 – A number will only be divided by two if there are 0, 2, 4, 6 and 8 anywhere within the figure. For example, number 130 is divisible by 2 because the last digit is 0, which makes the whole figure divisible by 2.

  • Tip 2 – One of the easiest tricks is to find if a number is divisible by 3 or not. When the digit of a figure is a multiple of 3, then the number is easily divisible by 3.

Now, for the concerned question, a student can quickly figure out which number can be divided by 6 by implementing the tips mentioned above. The NCERT Maths Class 6 Chapter 3 Solutions come handy for a better practice of these mathematical problems.

For a better understanding of the methods implemented within the chapter, a student can have a quick read of the other exercises. By learning other methods applied in the rest of the exercises, your preparations for upcoming exams becomes easy.

Exercise 4 is one of the simplest yet important exercises with the list. It comprises seven questions. The pattern of this specific exercise has been kept short and simple. Most of these questions are about finding common factors.

When you find factors of more than one number and arrive at a single factor for multiple numbers, they are known as ‘common factors’. For example, number 30 has 3, 5 and 6 as its factors and number 45 have 3, 5 and 9 as its factors. The digits 3 and 5 are the common factors of numbers 30 and 45.

There two questions in this exercise that deal with the divisibility test of 12. Just like the digit 6, if a figure is divisible by both 3 and 4, that number is divisible by 12. For example, number 36 is divisible by both 3 and 4. Hence, it is also divisible by 12. But, for numbers like 32, the numbers are divided only by 4 but not 3. Hence, it will not be divided by 12.

For a better understanding, our NCERT Solution for Class 6 Maths Chapter 3 Exercise 3.3 is crafted with utmost accuracy. These solutions follow the latest CBSE syllabus as per NCERT guidelines; hence they are updated given the curricular requirement for Maths Class 6. These solutions are written in a flawless and straightforward language to simplify the process of learning. Furthermore, our subject experts have poured in their years of experience and have made this handy guide as one of the best for students of Class 6.

D. NCERT Solutions for Class 6 Maths Chapter 3 exercise 3.3 – Question 4

The fourth question within the list is almost the same as the previous two questions. It deals with the divisibility of 11. There are 6 short sub-parts within this question. These sub-sections are incorporated to help students determine which figures are divisible by 11.

The solution also elaborates on a trick to determine which figures can be divided by 11. Here’s a gist of this shortcut technique.

A student has to add all digits from the odd places (from right) and even places (from right). After addition, they have to find the difference between the sums arrived at. If the difference is either 0 or divisible by 11, then the figures are divisible by 11.

For example, the number 1331 is divisible by 11. Here, you will add the numbers present in odd place value (1 + 3) = 4 and the total of the even place value (3 + 1) = 4. Now, subtracting these two will bring the result to 0 (4 – 4= 0). It thus establishes that the number is divisible by 11.

As for its relation with other exercises in the chapter, an overview of Exercise 3.5 gives an insight into these equations of divisibility. Have a brief look at it. The said exercise consists of 12 questions, most of which comprise a few sub-sections. Students must practice this exercise thoroughly as it incorporates various brain-teasers that improve their logical reasoning ability.

The first question within that list consists of nine questions. The patterns of these questions are simple as a student has to determine if the given statements are true or not.

The next question is represented as a factor tree. In this problem, a student has to find the missing factors of 60. It again emphasises on the learning of previous exercises. A student can easily determine the missing factors by applying quick tricks of divisibility taught in the previous exercise. 

To help students understand complex problems on numbers, these questions of Playing with Numbers are designed as a chart or tree. To simplify your learning and to understand this arrangement, our solutions have sufficiently provided easy examples of such sums. A student can practice these even in their leisure hours to gain mastery over solving such question patterns.

Next three questions in this set are related to prime factors. Before solving all questions on prime factors, it is beneficial to have an introduction to the topic.

Simply put, a prime factor is about figuring out which numbers are multiplied to make a whole number. For example, the prime numbers 5 and 7 make a whole number 35 when they are multiplied.

The remaining seven questions are a mixture of prime factorisation and divisibility. A student has to figure out which method is applicable to these questions for solving them accurately during exams. To complete the sums, a student can refer to the factor trees and arrive at accurate answers.

Our subject experts not only provide various examples but also accumulate their efforts and experience to make learning more interesting. The NCERT Solutions for Class 6 Maths Chapter 3 comprise different techniques of learning and fun ways of studying so that a student can practise the exercises at their ease. Our experienced writers have compiled accurate solutions as per the guidelines of NCERT and have given them a twist of fun learning to simplify learning for students.

E. Chapter 3 Maths Class 6 Exercise 3.3 – Question 5

The next question in line is in the form of filling in the blanks. A student has to find out the smallest digit and the largest digit and fill up the blank space to make the figure divisible by three. 

These sums are tricky and test the ability of a student. As these brain-teasers can be a regular occurrence in higher studies, it is essential to practice them to acquire an improved problem-solving ability. Hence, learning the various methods of divisibility is imperative. 

An overview of Chapter 3 can help a student gain an insight regarding the difficult sums they may face in this specific chapter and their higher studies. They can also gain a better understanding of such questions by following up with the 6th exercise within this chapter, which is regarding H.C.F. or Highest Common Factor.

A highest common factor or H.F.C is the highest number that happens to be common in a comparison between two or more digits. For example, figures 32 and 48 have the highest factor of 16 as it divides both 32 and 48 perfectly.

The complete antithesis of H.C.F. is L.C.M. Expanded as Lowest Common Multiple; LCM is the smallest positive number that factors a given set of numbers. With a clear understanding of these concepts, a student becomes confident to prepare the chapter Playing with Numbers for his/her exams.

Our quality solutions for Class 6th Maths Chapter 3 Exercise 3.3 provide the best examples for students, carefully drafted by our subject experts to instil a complete understanding of the concepts. 

These solutions are accurate given their drafting by expert tutors as per the NCERT guidelines. Our experts have also created new and fun ways of learning to make practising the chapter simple and easy. The PDF version of these solutions is easily available, and their free accessibility makes them a handy guide for students to have before their exams as per convenience.

F. Playing with Numbers Exercise 3.3 – Question 6

The last question of this exercise is tantamount to the previous section. It carries two sub-sections that are presented as per the increasing level of complexity. The question is about finding out the smallest and largest digit within the blank space, which should also make the total number divisible by 11.

The method of divisibility is important in this section. In a previous question, our solution explains a simple trick to determine which numbers can be divided by 11. A student can conveniently use this tip and figure out the answers to this section.

With rigorous practice, a student can easily master the simple tricks of Mathematics. It will enable them to prepare for the final exercise of this chapter. The 7th exercise is an accumulation of all previous concepts learnt in this chapter Playing with Numbers. Hence the question pattern of the 7th exercise isn’t short and simple; rather, they are explanatory.

This last exercise carries 11 questions which come as a combination of various concepts like divisibility, factors, prime numbers, H.C.F., L.C.M., etc.

The first, third and the seventh questions of the list are presented with a hint of complexity, but they are actually about figuring out the H.C.F. Rest of the questions mainly deal with the concept of L.C.M. The catch is that L.C.M. related questions incorporate multiple factors of the rest of the concepts discussed within the topic. Complete your exam preparation with Maths Chapter 3 Playing with Numbers solutions compiled by our subject experts. Students need to understand these undertones and proceed with a suitable approach accordingly.

For example, the fourth question in this exercise asks to determine the smallest 3-digit number, which is divisible by 6, 8 and 12. The methods of divisibility come handy in such cases and help to find out the smallest 3-digit number. Students thus need to calculate answers to such questions as per the suitable concepts applicable.

With the simple explanation given in our NCERT Maths Class 6 Chapter 3 Solutions and examples illustrated, our PDF files helps a student to acquire a lucid understanding of Mathematics as a subject. It also helps them learn several shortcut techniques for solving various questions related to numbers. 

Our solutions for Playing with Numbers Class 6 Questions are known to be among the best guide for a student’s complete exam preparation. Their easy availability online only makes them more accessible. These free PDFs have proven to be effective as we follow the latest syllabus of the CBSE board and guidelines drafted by NCERT. 


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We, at Vedantu, strive to provide the best quality solutions for CBSE students. Our subject experts have poured in their years of experience to make the solutions simple and interesting for the ease of a student’s learning. These solutions, available subject-wise for all classes, have helped students significantly in their exam preparations.

Class 6 Maths NCERT Solutions – Chapter 3 Playing with Numbers are solved by our expert tutors and have made this subject-oriented study material a handy guide. It consists of various examples and exercises for improved practice before exams. These solutions incorporate shortcut techniques of studying every subject, which not only makes learning interesting but also helps to prepare a student for their exams.

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So, why are you still waiting? Download your free PDF solution on Playing with Numbers today to join us on this exciting journey of learning.