NCERT Summary: Playing with Numbers

# Playing with Numbers Summary Class 6 Maths Del

 Table of contents Factors Multiples Prime and Composite Numbers Tests for Divisibility of Numbers Common Factors and Common Multiples Prime Factorisation Highest Common Factor Lowest Common Multiple Some More Divisibility Rules

## Factors

• A factor of a number is an exact divisor of that number.
• 1 is a factor of every number.
• Every number is a factor of itself.
• Every factor is less than or equal to the given number.
• Number of factors of a given number are finite.

## Multiples

• A number is said to be a multiple of any of its factors.
• Every multiple of a number is greater than or equal to that number.
• The number of multiples of a given number is infinite.
• Every number is a multiple of itself.

## Prime and Composite Numbers

• Prime numbers: Each of the numbers which have exactly two factors namely, 1 and the number itself, are called prime numbers, For example, 2, 3, 5, 7, 11, .... etc. 2 is the smallest prime number which is even. Every prime number except 2 is odd.
• Twin prime: Two consecutive odd prime numbers are known as twin prime. For example, 3 and 5.
• Prime triplet: A set of three consecutive prime numbers, differing by 2, is called a prime triplet. The only prime triplet is (3, 5, 7).
• Co-primes: Two numbers are said to be co-prime if they do not have a common factor other than 1. For example, 2 and 3. Any two prime numbers are always co-prime but converse is not always true.
• Composite numbers: The numbers having more than two factors are known as composite numbers.
For example, 4, 6, 8, 9, 10, 12, 14, .... etc. and 1 is neither prime nor composite because it has a single factor.
• Even number: All multiples of 2 are called even number.
• Odd number: Numbers which are not multiples of 2 are called odd numbers.

Question for NCERT Summary: Playing with Numbers
Try yourself:
What is a factor of a number?

## Tests for Divisibility of Numbers

A number is divisible by 2, if its unit digit are 0, 2, 4, 6 or 8.

• A number is divisible by 3, if the sum of its digits is divisible by 3.
• A number is divisible by 4, if the number formed by last two digits is divisible by 4.
• A number is divisible by 5, if its unit digit is 0 or 5.
• A number is divisible by 6, if the number is divisible by 2 and 3.
• A number is divisible by 8, if the number formed by last three digits is divisible by 8.
• A number is divisible by 9, if the sum of its digits is divisible by 9.
• A number is divisible by 11, if the difference of the sum of its digits in odd places and the sum of its digits in even places is either 0 or a multiple of 11.

## Common Factors and Common Multiples

• A factor which is common in two or more numbers is called common factor.
• A multiple which is common to two or more numbers is called common multiple.
• Co-prime are those number which have 1$1$ as common factors.

### Factor Tree

When we go on factorizing a number till we reach its ultimate factorisation and write the process as follows, we get the shape of a tree called Factor tree.
For example: Let us factorize 90. Let us see below:

Thus. 90 = 2 × 3 × 3 × 5.

## Prime Factorisation

The method of representing a number as a product of its factors is called prime factorization.

## Highest Common Factor

HCF of two or more numbers is the highest or greatest factor among all the common factors.

## Lowest Common Multiple

• LCM of two or more numbers is the lowest multiple among all the common multiples
• Simply, a product of the prime factors of two or more numbers is called LCM, counted by the maximum number of times they occur in any of the numbers.

## Some More Divisibility Rules

• If a number is divisible by another number then it is divisible by each of the factors of that number.
• If a number is divisible by two co-prime numbers then it is divisible by their product also.
• If two given numbers are divisible by a number, then their sum is also divisible by that number.
• If two given numbers are divisible by a number, then their difference is also divisible by that number.
The document Playing with Numbers Summary Class 6 Maths Del is a part of the Class 6 Course Mathematics (Maths) Class 6.
All you need of Class 6 at this link: Class 6

## Mathematics (Maths) Class 6

134 videos|325 docs|42 tests

## FAQs on Playing with Numbers Summary Class 6 Maths Del

 1. What are the important concepts covered in the NCERT Class 6 Mathematics chapter "Playing with Numbers"?
Ans. The chapter "Playing with Numbers" in NCERT Class 6 Mathematics covers concepts such as factors and multiples, prime and composite numbers, tests of divisibility, and applications of divisibility rules.
 2. How can I determine if a number is divisible by 2, 3, 5, 9, or 10 without dividing it?
Ans. To determine if a number is divisible by 2, it should end with an even digit (0, 2, 4, 6, or 8). For divisibility by 3, sum up the digits of the number, and if the sum is divisible by 3, then the number is also divisible by 3. Similarly, for divisibility by 5, the number should end with 0 or 5. For divisibility by 9, sum up the digits of the number, and if the sum is divisible by 9, then the number is also divisible by 9. For divisibility by 10, the number should end with 0.
 3. Can you explain what prime and composite numbers are?
Ans. Prime numbers are numbers greater than 1 that only have two factors, 1 and the number itself. For example, 2, 3, 5, 7, and 11 are prime numbers. Composite numbers, on the other hand, have more than two factors. They can be divided evenly by numbers other than 1 and themselves. For example, 4, 6, 8, 9, and 10 are composite numbers.
 4. How are factors and multiples related?
Ans. Factors and multiples are related as follows: A number is a factor of another number if it divides the number completely without leaving a remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4. On the other hand, a number is a multiple of another number if it can be obtained by multiplying the other number by an integer. For example, 12 is a multiple of 3 because 3 x 4 = 12.
 5. Can you provide some real-life examples where knowledge of factors and multiples is useful?
Ans. Knowledge of factors and multiples is useful in various real-life scenarios. For example: - In a school, the timetable is created by considering the common multiples of different subjects' periods. - In a supermarket, products are often packed in sets or multiples to make pricing and selling more convenient. - In construction, knowledge of factors helps in determining the number of tiles or bricks required to cover a given area without wastage. - In music, factors and multiples are used to understand harmonics and create chords.

## Mathematics (Maths) Class 6

134 videos|325 docs|42 tests

### Up next

 Explore Courses for Class 6 exam

### Top Courses for Class 6

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;