Class 6 Maths Exercise 3.4 Chapter 3 Playing With Numbers Solutions

NCERT Solutions Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.4 are provided here. These solutions are prepared by expert teachers to guide you in your exam preparation. The solutions are always prepared by following NCERT guidelines, so that it covers the whole syllabus accordingly. Our CBSE Class 6 Maths Solutions Chapter 3 Exercise 3.4 Solutions are very helpful in scoring well in examinations.

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Exercise 3.4

EXERCISE 3.4

Question 1:  Find the common factors of:

(a) 20 and 28        
(b) 15 and 25        
(c) 35 and 50        
(d) 56 and 120

Solution:
(a) Given numbers are: 20 and 28
Factors of 20 are 1, 2, 4, 5, 10, 20
Factors of 28 are 1, 2, 4, 7, 28
Hence, the common factors are 1, 2 and 4.

(b) Given numbers are: 15 and 25
Factors of 15 are 1, 3, 5, 15
Factors of 25 are 1, 5, 25
Hence, the common factors are 1 and 5.

(c) Given numbers are: 35 and 50
Factors of 35 are: 1, 5, 7, 35
Factors of 50 are: 1, 2, 5, 10, 50
Hence, the common factors are 1 and 5.

(d) Given numbers are: 56 and 120
Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, 120
Hence, the common factors are 1,2, 4, and 8.

Question 2:  Find the common factors of:
(a) 4, 8 and 12      
(b) 5, 15 and 25

Solution:
(a) 4, 8 and 12
1, 2, 4 are factors of 4
1, 2, 4, 8 are factors of 8
1, 2, 3, 4, 6, 12 are factors of 12
Common factors = 1, 2, 4

(b) 5, 15 and 25
1, 5 are factors of 5
1, 3, 5, 15 are factors of 15
1, 5, 25 are factors of 25
Common factors = 1, 5

Question 3:  Find first three common multiples of:
(a) 6 and 8             
(b) 12 and 18

Solution:

(a) 6 and 18
6, 12, 18, 24, 30 are multiples of 6
8, 16, 24, 32 are multiples of 8
Three common multiples are 24, 48, 72

(b) 12 and 18
12, 24, 36, 48 are multiples of 12
18, 36, 54, 72 are multiples of 18
Three common factors are 36, 72, 108

Question 4: Write all the numbers less than 100 which are common multiples of 3 and 4.

Solution:
Multiples of 3 are 3, 6, 9, 12, 15
Multiples of 4 are 4, 8, 12, 16, 20
Common multiples are 12, 24, 36, 48, 60, 72, 84 and 96

Question 4:  Which of the following numbers are co-prime?

(a) 18 and 35        
(b) 15 and 37        
(c) 30 and 415      
(d) 17 and 68        
(e) 216 and 215   
(f) 81 and 16

Solution:
(a) 18 and 35
Factors of 18 are 1, 2, 3, 6, 9, 18
Factors of 35 are 1, 5, 7, 35
Common factor = 1
Since, their common factor is 1.
Hence, the given two numbers are co-prime

(b) 15 and 37
Factors of 15 are 1, 3, 5, 15
Factors of 37 are 1, 37
Common factors = 1
Since, their common factor is 1.
Hence, the given two numbers are co-prime

(c) 30 and 415
Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
Factors of 415 are 1, 5, 83, 415
Common factors = 1, 5
Since, their common factor is other than 1.
Hence, the given two numbers are not co-prime

(d) 17 and 68
Factors of 17 are 1, 17
Factors of 68 are 1, 2, 4, 17, 34, 68
Common factors = 1, 17
Since, their common factor is other than 1.
Hence, the given two numbers are not co-prime

(e) 216 and 215
Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54
Factors of 215 are 1, 5, 43, 215
Common factors = 1
Since, their common factor is 1.
Hence, the given two numbers are co-prime

(f) 81 and 16
Factors of 81 are 1, 3, 9, 27, 81
Factors of 16 are 1, 2, 4, 8, 16
Common factors = 1
Since, their common factor is 1.
Hence, the given two numbers are co-prime

Question 6:  A number is divisible by both 5 and 12. By which other number will that number be always divisible?

Solution: Factors of 5 are 1, 5
Factors of 12 are 1, 2, 3, 4, 6, 12
Their common factor = 1
Since, their common factor is 1.
The given two numbers are co-prime and is also divisible by their product 60
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Question 7:  A number is divisible by 12. By what other numbers will that number be divisible?

Solution: Since, the number is divisible by 12.
Hence, it also divisible by its factors
i.e., 1, 2, 3, 4, 6, 12
Therefore 1, 2, 3, 4, 6 are the numbers other than 12 by which this number is also divisible

Access NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers – All Exercises

Below we have provided the links to check solutions of the other exercises of the chapter.

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