Exam - Focused Revision Notes for CBSE Class 7 Maths Chapter 2 - Fractions and Decimals
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Access Class 6 Mathematics Chapter 3 – Playing with Numbers Notes in 30 Minutes
Factors And Multiples
If a number $n$ is the exact divisor of the number $m$ then $n$ is the factor of $m$ i.eThe factor of a number is the exact divisor of that number.
A number always has at least two factors i.e., $1$ and the number itself.
Every factor is less than or equal to the given number and is finite.
For example: Factors of $20$ are $2,10,5$ and $4$
A perfect number is whose sum of all the factors is equal to twice the number.
Multiple is the product of two or more numbers
A number always have at least one multiple i.e., the number itself
Multiples is always greater than or equal to the given number and multiples of a number is infinite.
For example: $5\times 4=20$ here $20$ is the multiple of $5$ and $4$
Prime And Composite Numbers
Prime numbers are the numbers which are divisible only by $1$ and the number itself i.e., a prime number always have only two factors.
$2$ is the only prime number which is even and all other prime numbers are odd.
For example: $2,3,5,7,11,13,17$ etc. are the prime numbers
Composite numbers are the numbers which are divisible by more than two factors i.e., composite number have more than two factors.
For example: $4,6,8,10,12,14,$ etc.
$1$ has only one factor i.e., $1$ itself so it is neither prime nor composite number.
Even numbers are those number which are the multiples of $2$
Odd numbers are those number which are not the multiples of $2$
Test for Divisibility of Numbers
1. Divisibility by $10$
A number is divisible by $10$ when its ones digit is $0$ then only it is the multiple of $10$
For example: $520,950,630,20$ etc.
2. Divisibility by $5$
A number is divisible by $5$ when its ones digit is either $0$ or $5$ then only it is the multiple of $5$
For example: $50,95,65,20$ etc.
3. Divisibility by $2$
A number is divisible by $2$ when its one’s digit is $0,2,4,6$ or $8$ i.e., every even number is divisible by $2$
For example: $50,92,64,26,68$ etc.
4. Divisibility by $3$
A number is divisible by $3$ when sum of its digit is divisible by $3$
For example: $7263$, the sum of digits of $7263$ is $18$ and $18$ is divisible by $3$ therefore $7263$ is also divisible by $3$
5. Divisibility by $6$
A number is divisible by $6$ only if it is divisible by $2$ and $3$ both.
For example: $6,12,18,24,36$ etc.
6. Divisibility by $4$
One digit and two-digit number divisibility by $4$ is checked by actual division.
But three or more-digit number is divisible by $4$ if the number formed by the last two digit is divisible by $4$
For example: $1000,3012,523612$ etc.
7. Divisibility by $8$
One digit to three-digit number divisibility by $8$ is checked by actual division.
But four or more-digit number is divisible by $8$ if the number formed by the last three digit is divisible by $8$
For example: $1000,3012,523612$ etc.
8. Divisibility by $9$
A number is divisible by $9$ when sum of its digit is divisible by $9$
For example: $215847$, the sum of digits of $215847$ is $27$ and $27$ is divisible by $9$ therefore $215847$ is also divisible by $9$
9. Divisibility by $11$
If the difference between the sum of the digits at odd places and the sum of the digits at even places of the number is either $0$ or divisible by $11$, then the number is divisible by $11$
Sum of digits at odd places$=6+8+9=23$
Sum of digits at even places$=1+0=1$
Now, difference between the sum of the digits at odd places and the sum of the digits at even places$=23-1=22$
Since, $22$ is divisible by $11$
Therefore, $61809$ is also divisible by $11$
Common Factor Or Common Multiple
A factor which is common in two or more numbers is called common factor.
Factors of $8$ are $1,2,4$ and $8$
Factors of $12$ are $1,2,3,4,6$and $12$
$\therefore 4$ is the common factor of $8$ and $12$
A multiple which is common to two or more numbers is called common multiple.
Multiple of $2$ are $4,6,8,10,12$ and $18$
Multiple of $3$ are $6,9,12,15,18$ and $21$
$\therefore 6,12$ and $18$ are common multiple of $2$ and $3$
Co-primeare those number which have $1$ as common factors.
For example: $5,8,69,52,41$ etc. are co-primes
Some More Divisibility Rules
If a number is divisible by another number, then it is divisible by each of the factors of that number.
For example: $12$ is divisible by $6$
Factors of $6$ are $1,2,3$and $6$
Therefore, $12$ is also divisible by $1,2$ and $3$
If a number is divisible by two co-prime numbers, then it is divisible by their product also.
$160$ is divisible by $8$ and $5$ which are co-primes
Product of $8$ and $5$ is $40$
Therefore, $160$ is also divisible by $40$
If two given numbers are divisible by a number, then their sum is also divisible by that number.
$15$ and $10$ are divisible by $5$
Sum of $15$ and $10$ is $25$ which is also divisible by $5$
If two given numbers are divisible by a number, then their difference is also divisible by that number
$15$ and $10$ are divisible by $5$
Difference of $15$ and $10$ is $5$ which is also divisible by $5$
The method of representing number as a product of its factors is called prime factorization.
For example: $36$ can be written as $2\times 2\times 3\times 3$, $2$ and $3$ are prime numbers.
Highest Common Factor
HCF of two or more number is the highest or greatest factor among all the common factors.
Factors of $60$ are $2\times 2\times 3\times 5$
Factors of $28$ are $2\times 2\times 3\times 7$
Common factors are: $2$ and $3$
Highest common factor is $3$
Lowest Common Multiple
LCM of two or more number is the lowest multiple among all the common multiples
Simply, product of the prime factors of two or more number is called LCM counted the maximum number of times they occur in any of the numbers.
Prime factorization of $30$ is $2\times 3\times 5$
Prime factorization of $4$ is $2\times 2$
LCM of $15$ and $4$ is $2\times 2\times 3\times 5=60$
Revision Notes for CBSE Class 6 Maths Chapter 3 - Free PDF Download
The chapter has seven exercises that include types of numbers, factors and their properties, multiples, prime and composite numbers, divisibility test of numbers, common multiples, common factors, prime factorisation, highest common factor, lowest common multiple and some practising problems based on LCM and HCF.
There are revision questions for practice related to all the topics mentioned above. These problems have been divided into 7 exercises from 3.1 to 3.7 for the students to identify the topics easily.
Introduction To CBSE Class 6 Maths Revision Notes
Introduction to CBSE Class 6 Maths Before you download the PDF, read some of those points that we have stated below. These are very basic revision notes and once you download the PDF, you will have more significant insights into the subject and there are high chances that you will perform better.
Playing With Numbers Class 6 Notes Revision notes that Vedantu provides will help you in understanding the core parts of that particular chapter and let you prepare well for the exam that you’ll be appearing in.
Class 6 Maths Chapter 3 Revision Notes
Our practise papers usually allow you to understand the pattern and the weightage of the subject and help you practice the same. In addition, we also add the important questions from the previous years so that you can master the subject before you appear for the examination.
A number is defined as an arithmetical value, expressed by words, symbols, and figures. These numbers can be written either in single-digit format, double digits format, the three-digits format in the generalized form.
1. Types of Numbers
A number system is a system of writing the expression of numbers. According to the number system, there are different types of numbers. They are:
A factor of a number is a divisor of the number itself.
Example: 3, 4, 6, 9, 12, and 36 are the factors of 36.
3. Properties of Factors
1 is a factor of every number.
Every number is a factor of itself.
Every factor of a number is an exact division of that number.
Every factor of a given number is greater than or equal to the number.
4. Perfect Numbers
A perfect number is one of the types of numbers that has the sum of all the factors equal to twice the number.
Example: Factors of 56: 1, 2, 4, 7, 14, 28, and 56
Here, 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 x 8
Therefore, the sum of factors of 28 is equal to twice the number of 28.
Multiples of a number are those numbers that we get on multiplying the number by an integer.
Examples: Multiples of 3 are 6,9,12,15,18 etc.
6. Properties of Multiples
There are infinite multiples of a given number.
Every number is a multiple of itself.
7. Prime Numbers
The numbers whose factors are 1 and the number itself are called Prime numbers.
Example: 2, 3, 5, 7 etc.
8. Composite Numbers
Numbers having multiple factors are called Composite numbers.
Example: 4, 6, 8 etc.
Divisible by 2 or 5 or both 2 and 5.
9. Divisibility Tests
Divisibility Test for 2
Divisibility Test for 4
Divisibility Test for 3
Divisibility Test for 5
Divisibility Test for 8
Divisibility Test for 6
Divisibility Test for 7
Divisibility Test for 9
Divisibility Test for 10
Divisibility Test for 11
10. Common Factor
1. Common Multiples
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Expert Tips on CBSE Class 6 Exam Preparation
Have a positive attitude towards the exam
Set a deadline for each topic. This will help to finish all the subjects within the time.
After you have completed studying, you must revise all that you have already studied.
Set your studying schedule and pick a peaceful place to study.
Set some time to refresh your memory. So, do some engaging activities regularly.
Ensure that you have enough sleep time
Before the exam, do not read any new topic rather stay stress-free, relaxed and calm while answering the questions.
Vedantu's "Playing With Numbers" Class 6 Notes for CBSE Maths Chapter 3 provide a comprehensive and valuable resource for students. The free PDF download offers an excellent opportunity for learners to enhance their mathematical skills in an engaging manner. The notes cover fundamental concepts, techniques, and practical examples, enabling students to grasp the topic with clarity. Vedantu's commitment to quality education is evident through these well-structured and accessible materials. By utilizing these resources, students can develop a solid foundation in number theory and problem-solving, empowering them to tackle more advanced mathematical challenges with confidence. Overall, Vedantu's Class 6 Notes serve as an invaluable aid in fostering a love for mathematics and promoting academic success.
FAQs on Playing With Numbers Class 6 Notes CBSE Maths Chapter 3 (Free PDF Download)
Q1. Does Vedantu Charge You Any Amount of Money to Access the Revision Notes?
Ans: No. Vedantu’s Class 6 Maths Chapter 3 notes are available free of cost. In order to help most students prepare for this subject and score good marks in your Examinations. Notes on playing with numbers class 6 can be downloaded free of cost from Vedantu’s Website.
Q2. How Can Vedantu’s Chapter 3 Class 6 Maths Playing with Numbers Notes Help You?
Ans: Playing with numbers, class 6 notes of Vedantu provides will help you in:
Understanding the core parts of that particular chapter
Let you prepare well for the exam beforehand.
Practice papers can help you to know the pattern and the weightage of the subject.
Vedantu has added some important questions from the previous years so that you can master the subject before you appear for the examination.
Q3. How to Make the Best Utilization of Study Time? List Out Some Resolutions and Strategies.
Ans: Here are some effective time management tips for CBSE Class 6 students:
Study in shorter bursts
Do not do multitasking
Make a project plan
It would help if you start your assignments as soon
Set goals for study
Remove all kinds of distractions
Use an agenda
Build a master schedule
4. What are the different types of numbers that are discussed in Chapter 3 of the CBSE Class 6 Maths textbook?
The different types of numbers that are discussed in Chapter 3 of the CBSE Class 6 Maths textbook are natural numbers, whole numbers, integers, and rational numbers.
Natural numbers are the numbers that we use for counting. They are the numbers from 1 to infinity.
Whole numbers are the numbers that include natural numbers and zero. They are the numbers from 0 to infinity.
Integers are the numbers that include whole numbers, negative whole numbers, and zero. They are the numbers from negative infinity to infinity.
Rational numbers are the numbers that can be expressed as a fraction of two integers. They are the numbers from negative infinity to infinity.
5. What is the difference between a prime number and a composite number?
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A composite number is a natural number that is not a prime number.
For example, 2 is a prime number because it is greater than 1 and it is not a product of two smaller natural numbers. 6 is a composite number because it is a product of two smaller natural numbers, 2 and 3.