NCERT Solution for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4
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Board CBSE
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TextBook NCERT
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CLASS Class 6
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SUBJECT Maths
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CHAPTER Chapter 3
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SUBJECT Playing with Numbers
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Visit NCERT Solutions
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NCERT Class 6 Chapter 3 Ex 3.1
NCERT Class 6 Chapter 3 Ex 3.2
NCERT Class 6 Chapter 3 Ex 3.3
NCERT Class 6 Chapter 3 Ex 3.5
NCERT Class 6 Chapter 3 Ex 3.6
NCERT Class 6 Chapter 3 Ex 3.7
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NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4 with Answers
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
Answer 1:
(a) 20=1×20
=2×10
=4×5
28=1×28
=2×14
=4×7
Factors of 20 = 1, 2, 4, 5, 10, 20
Factors of 28 = 1, 2, 4, 7, 14, 28
Common factors = 1, 2, 4
(b)15 =1×15
=3×5
25=1×25
=5×5
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors = 1, 5
(c) 35=1×35
=5×7
50=1×50
=2×25
=5×10
Factors of 35 = 1, 5, 7, 35
Factors of 50 = 1, 2, 5, 10, 25, 50
Common factors = 1, 5
(d) 56=1×56
=2×28
=4×14
=7×8
120=1×120
=2×60
=3×40
=4×30
=5×24
=6×20
=8×15
=10×12
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56
Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 60, 120
Common factors = 1, 2, 4, 8
Question 2:
Find the common factors of:
(a) 4, 8 and 12 (b) 5, 15 and 25
Answer 2:
(a) 4=1×4
=2×2
8=1×8
=2×4
12=1×12
=2×6
=3×4
Factors of 4 = 1, 2, 4
Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Common factors of 4, 8 and 12 = 1, 2, 4
(b) 5=1×5
15=1×15
=3×5
25=1×25
=5×5
Factors of 5 = 1, 5
Factors of 15 = 1, 3, 5, 15
Factors of 25 = 1, 5, 25
Common factors of 5, 15 and 25 = 1, 5
Question 3:
Find the first three common multiples of:
(a) 6 and 8 (b) 12 and 18
Answer 3:
(a) Multiple of 6 = 6, 12, 18, 24, 30, 36, 42, 28, 54, 60, 72, …………
Multiple of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, …………………….
First three common multiples of 6 and 8 = 24, 48, 72
(b) Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ………
Multiple of 18 = 18, 36, 54, 72, 90, 108, ………………………………
The first three common multiples of 12 and 18 = 36, 72, 108
Question 4:
Write all the numbers less than 100 which are common multiples of 3 and 4.
Answer 4:
Multiple of 3 less than 100 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99
Multiple of 4 less than 100 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100
Common multiples of 3 and 4 which are less than 100= 12, 24, 36, 48, 60, 72, 84, 96
Question 5:
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
Answer 5:
(a) 18=1×18
=2×9
=3×6
35=1×35
=5×7
Factors of 18 = 1, 2, 3, 6, 9, 18
Factors of 35 = 1, 5, 7, 35
Common factor = 1
Since, both have only one common factor, i.e., 1, therefore, they are co-prime
numbers.
(b) 15=1×15
=3×5
37=1×37
Factors of 15 = 1, 3, 5, 15
Factors of 37 = 1, 37
Common factor = 1
Since, both have only one common factor, i.e., 1, therefore, they are co-prime
numbers.
(c) 30=1×30
=2×15
=3×5
415=1×415
=5×83
Factors of 30 = 1, 2, 3, 5, 6, 15, 30
Factors of 415 = 1, 5, 83, 415
Common factor = 1, 5
Since, both have more than one common factor, therefore, they are not coprime
numbers.
(d)17=1×17
68=1×68
=2×34
=4×17
Factors of 17 = 1, 17
Factors of 68 = 1, 2, 4, 17, 34, 86
Common factor = 1, 17
Since, both have more than one common factor, therefore, they are not co-prime
numbers.
(e) 216=1×216
=2×108
=3×72
=4×54
=6×36
=8×27
=9×24
=12×18
Factors of 216 = 1, 2, 3, 4, 6, 8,9,12,18,36,54, 72, 108, 216
Factors of 215 = 1, 5, 43, 215
Common factor = 1
Since, both have only one common factor, i.e., 1, therefore, they are co-prime
numbers.
(f)81=1×81
=3×27
=9×9
16=1×16
=2×8
=4×4
Factors of 81 = 1, 3, 9, 27, 81
Factors of 16 = 1, 2, 4, 8, 16
Common factor = 1
Since, both have only one common factor, i.e., 1, therefore, they are co-prime
numbers.
Question 6:
A number is divisible by both 5 and 12. By which other number will that number be
always divisible?
Answer 6: 5=1×5
12=2×2×3
LCM= 5×2×2×3 = 60
The number is divisible by both 5 and 12 is 60.
60=1×60
=2×30
=3×20
=4×15
=5×12
=6×10
The number by which 60 are divisible are 1,2,3,4,6,10,15,20,30,60.
Question 7:
A number is divisible by 12. By what other numbers will that number be divisible?
Answer 7:
12=1×12
=2×6
=3×4
Factors of 12 = 1, 2, 3, 4, 6,12.
Therefore, the number is also divisible by 1, 2, 3,4 and 6.
NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.4
