NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.1

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.1 (Ex. 3.1) Playing with Numbers updated for CBSE and State board student academic session 2021-2022. Videos related to 6th Math ex.

3.1 is also given in solution as well as explanation format, where each question is explained properly.

Class 6 Maths Chapter 3 Exercise 3.1 Solution




Class: 6Mathematics
Chapter: 3Playing with Numbers
Exercise: 3.1NCERT Solution in Hindi and English

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Class 6 Maths Chapter 3 Exercise 3.1 Solution in Videos

Class 6 Maths Chapter 3 Exercise 3.1 Solution
Class 6 Maths Chapter 3 Exercise 3.1 Explanation




Factors and Multiples

Factor:

A factor of a number is an exact divisor of that number. In other words, a factor of a number is that number which completely divides the number without leaving a remainder.
Example: We know that, 12 = 4 × 3, 12 = 2 × 6, also, 12 = 1 × 12
This shows that each of the numbers 1, 2, 3, 4, 6 and 12 exactly divides 12.
Therefore, 1, 2, 3, 4, 6 and 12 are all factors of 12.

Multiple:

A multiple of a number is a number obtained by multiplying it by a natural number.
If we multiply 2 by 1, 2, 3, 4, … , we get 2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6, 2 × 4 = 8, … .
Thus, 2, 4, 6, 8, … are multiples of 2.
Clearly, a number is a multiple of each of its factors.



Properties of Factors and Multiples

Property 1: 1 is a factor of every number

We have, 1 = 1 × 1; 2 = 1 × 2; 3 = 1 × 3; 9 = 1 × 9 and so on. Thus, 1 is a factor of every number.

Property 2: Every number is a factor of itself

We have, 1 = 1 × 1; 4 = 4 × 1; 12 = 12 × 1; 67 = 67 × 1 and so on.
We can express every number in this way. Hence, every number is a factor of itself.

Property 3: Every factor of a number is less than or equal to the number

Factors of 21 are 1, 3, 7 and 21 itself. Out of these numbers 21, itself is the largest factor and all other factors are less than 21.
The above property is also evident from the fact that divisors of a number are less than or equal to the number itself.

Property 4: Factors of a given number are finite

By property 3, every factor of a number is less than or equal to the number.
Hence, factors of a given number are finite.

Property 5: Every multiple of a number is greater than or equal to that number

Multiples of 3 are 3, 6, 9, 12, 15, ….
In fact, multiplies of a number are obtained by multiplying the number by 1, 2, 3, 4, 5, …. Therefore, the smallest multiple of a number is the number itself. Hence, every multiple of a number is greater than or equal to the number itself.

Property 6: Every number is a multiple of itself

We have, 5 = 5 × 1; 13 = 13 × 1; 18 = 18 × 1 and so on.
So, every number is a multiple of itself.

Property 7: The number of multiples of a given number is infinite

Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, …. Clearly, it is a never ending list.
Hence, the number of multiples of a given number is infinite.



Types of Numbers

(i) Even Numbers:

All multiples of 2 are called even numbers.
Example: 2, 4, 6, 8, 10, 12, 14 etc. are all even numbers.

(ii) Odd Numbers:

Numbers which are not multiples of 2 are called odd numbers.
Example: 1, 3, 5, 7, 9, 11, 13, 15 etc. are all odd numbers.

(iii) Perfect Numbers:

If the sum of all the factors of a number is two times the number, then the number is called a perfect number.
Example: 6 is a perfect number, since the factors of 6 are 1, 2, 3, 6 and (1 + 2 + 3 + 6) = (2 × 6). 28 is a perfect number, since the factors of 28 are 1, 2, 4, 7, 14, 28 and (1 + 2 + 4 + 7 + 14 + 28) = (2 × 28).

(iv) Prime Numbers:

Each of the numbers which has exactly two factors, namely, 1 and itself, is called a prime number.
Example: The numbers 2, 3, 5, 7, 11, 13, 17 etc. are all prime numbers.

(v) Co-prime Numbers:

Two numbers are said to be co-prime numbers if they do not have a common factor other than 1.
Example: (2, 3); (3, 4); (5, 6); (8, 13) etc. are pairs of co-prime numbers.

Note: Any two prime numbers are always co-primes, but two co-primes need not be both prime numbers. For example, 14, 15 are co-primes, while none of 14 and 15 is a prime number.




(vi) Composite Numbers:

Numbers having more than two factors are known as composite numbers.
Each of the numbers 4, 6, 8, 9, 10, 12, 14, 15, …are composite numbers.

(vii) Twin Primes:

Two prime numbers which have only one composite number between them are called twin primes.
Example: 3, 5; 5, 7; 11, 13 and 17, 19 etc. are pairs of twin primes between 1 and 20.

Class 6 Maths Exercise 3.1 Important Questions

What are prime numbers? List all prime numbers between 1 and 25.

Prime Numbers:
Each of the numbers which has exactly two factors, namely, 1 and itself, is called a prime number. In other words, we can say that prime numbers are only divisible by 1 or itself. Prime numbers between 1 and 25.
Example: The numbers 2, 3, 5, 7, 11, 13, 17, 19, 23 are all prime numbers lies between 1 and 25.

What is the smallest prime number? Is it an even number?

The smallest prime number is 2. Yes, it is an even number.

What are composite numbers? Can a composite number be odd? If yes, write the smallest odd composite number.

Numbers having more than two factors are known as composite numbers.
Each of the numbers 4, 6, 8, 9, 10, 12, 14, 15, …are composite numbers.
Yes, a composite number can be odd. The smallest odd composite number is 9.

What are twin-primes? Write all pairs of twin-primes between 1 and 20.

a pair of prime numbers (such as 3 and 5 or 11 and 13) differing by two.
All pairs of twin-primes between 1 and 20 are 3 and 5, 5 and 7, 11 and 13, 17 and 19.

(viii) Prime Triplet:

A set of three consecutive prime numbers which have only one composite number between each two of them are called prime triplet.
Example: 3, 5, 7 is the only prime triplet.

Some Important Facts

(i) 1 is neither prime nor composite.
(ii) 2 is the smallest prime number.
(iii) 2 is the only even prime number.
(iv) All other even numbers are composite numbers.

Class 6 Maths Exercise 3.1 Extra Questions with Answers

What are co-primes? Give examples of four pairs of co-primes. Are co-primes always prime? If no, illustrate your answer by an example.

Co-prime Numbers:
Two numbers are said to be co-prime numbers if they do not have a common factor other than 1.
Example: (2, 3); (3, 4); (5, 6); (8, 13) etc. are pairs of co-prime numbers.
Any two prime numbers are always co-primes, but two co-primes need not be both prime numbers. For example, 14, 15 are co-primes, while none of 14 and 15 is a prime number.

what is the factor of a number? Give an example.

A factor of a number is an exact divisor of that number. In other words, a factor of a number is that number which completely divides the number without leaving a remainder.
Example: We know that, 12 = 4 × 3, 12 = 2 × 6, also, 12 = 1 × 12

Define composite numbers.

Numbers having more than two factors are known as composite numbers.
Each of the numbers 4, 6, 8, 9, 10, 12, 14, 15, …are composite numbers.

List all the prime numbers between 40 and 60.

The prime numbers between 40 and 60 are: 41, 43, 47, 53, 59.

NCERT Solutions for Class 6 Maths Chapter 3 exercise 3.1 in english medium
Class 6 Maths Chapter 3 Exercise 3.1 in hindi medium
6 maths 3.1 in hindi