The DAV Class 5 Maths Book Solutions Pdf and **DAV Class 5 Maths Chapter 3 Brain Teasers** Solutions of Multiples and Factors offer comprehensive answers to textbook questions.

## DAV Class 5 Maths Ch 3 Brain Teasers Solutions

Question 1.

Tick (✓) the correct answer.

(a) Which of the following is not a factor of 48?

(i) 6

(ii) 7

(iii) 12

(iv) 48

Solution:

Factor of 48

6 × 8 = 48

12 × 4 = 48

48 × 1 = 48

7 × ? = ?

Option (ii) is the answer.

(b) Which of the following is a prime number?

(i) 91

(ii) 57

(iii) 97

(iv) 81

Solution:

A prime number is a number that has only two factors: 1 and the number itself.

91 = 1 × 7 × 13 × 91

57 = 1 × 3 × 19 × 57

97 = 1 × 97

81 = 1 × 3 × 9 × 27 × 81

So 97 has only two factors.

Option (iii) is the answer.

(c) The LCM of 10, 20, 25 is

(i) 20

(ii) 50

(iii) 100

(iv) 75

Solution:

Prime factorisation of 10 = 2 × 5

Prime factorisation of 20 = 2 × 2 × 5

Prime factorisation of 25 = 5 × 5

LCM of 10, 20, 25 = 2 × 2 × 5 × 5 = 100

Option (iii) is the answer.

(d) The prime factorisation of 36 is

(i) 4 × 3 × 3

(ii) 2 × 2 × 9

(iii) 12 × 3

(iv) 2 × 2 × 3 × 3

Solution:

Prime factorisation of 36 = 2 × 2 × 3 × 3

So option (iv) is the answer.

(e) 48 has ____ factors.

(i) 10

(ii) 8

(iii) 1

(iv) 6

Solution:

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 14, 18

Hence, there are 10 factors of 48.

So option (i) is the answer.

Question 2.

Write the first four multiples of:

(a) 1

Solution:

7 = 7, 14, 21, 28

(b) 9

Solution:

9 = 9, 18, 27, 36

(c) 12

Solution:

12 = 12, 24, 36, 48

(d) 1

Solution:

1 = 1, 2, 3, 4

(e) 13

Solution:

13 = 13, 26, 39, 52

Question 3.

Fill in the blanks.

(a) 2 × 3 × 7 = 42; 42 is a multiple of ____, _____, and _____.

Solution:

2, 3 and 7

(b) Fifth multiple of 9 : ______

Solution:

45

(c) Is 48 a multiple of 6? _______ (Yes/No)

Solution:

Yes

(d) Least multiple of 65 is ________

Solution:

65

(e) 7 × 3 = 21 : ______ and _____ are factors of _______.

Solution:

7, 3, 21

(f) Is 8 a factor of 70? ______ (Yes/No)

Solution:

No

(g) Is 1 a prime number? ______ (Yes/No)

Solution:

No

Question 4.

Find the factors of the following:

(a) 27

Solution:

27 = 1, 3, 9, 27

(b) 90

Solution:

90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

(c) 38

Solution:

38 = 1, 2, 19, 38

(d) 40

Solution:

40 = 1, 2, 4, 5, 8, 10, 20, 40

Question 5.

Is 217 divisible by 27?

Solution:

No, 217 is not divisible by 27.

Question 6.

Using Factor Tree Method, find the prime factorisation of the following:

(a) 30

Solution:

Prime factorisation of 30 = 2 × 3 × 5

(b) 84

Solution:

Prime factorisation of 84 = 2 × 2 × 3 × 7

Question 7.

Using Division Method, find the prime factorisation of the following:

(a) 36

Solution:

Prime factorisation of 36 = 2 × 2 × 3 × 3

(b) 74

Solution:

Prime factorisation of 74 = 2 × 37

Question 8.

Find the LCM of:

(a) 28 and 42

Solution:

Prime factorisation of 28 = 2 × 2 × 7

Prime factorisation of 42 = 2 × 3 × 7

LCM of 28 and 42 = 2 × 2 × 3 × 7 = 84

(b) 10 and 95

Solution:

Prime factorisation of 10 = 2 × 5

Prime factorisation fo 95 = 5 × 19

LCM of 10 and 5 = 2 × 5 × 19 = 190

Question 9.

How many even numbers are there between 20 and 50?

Solution:

22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48

even numbers between 20 and 50 = 14 numbers

Question 10.

Write all prime numbers between 50 and 80.

Solution:

Prime number between 50 and 80 = 53, 59, 61, 67, 71, 73, 79.

Question 11.

Write any five odd multiples of 3.

Solution:

5 odd multiples of 3 = 3, 9, 15, 21, 27

Additional Questions:

Question 1.

Write the next five multiples of the number given below:

(a) 10, 20, 30, ____, ____, ____, ____, ____,

Solution:

40, 50, 60, 70, 80

(b) 12, 24, 36, ____, ____, ____, ____, ____,

Solution:

48, 60, 72, 84, 96

(c) 13, 26, 39, ____, ____, ____, ____, ____,

Solution:

54, 65, 78, 91, 104

(d) 17, 34, 51, ____, ____, ____, ____, ____,

Solution:

68, 85, 102, 119, 136

(e) 19, 38, 57, ____, ____, ____, ____, ____,

Solution:

76, 95, 114, 133, 152

Question 2.

Find the LCM in each case.

(a) 14, 35

Solution:

14, 35

Prime factorisation of 14 = 2 × 7

Prime factorisation of 35 = 5 × 7

LCM of 14 and 35 = 7

(b) 8, 10, 20

Solution:

8, 10, 20

Prime factorisation of 8 = 2 × 2 × 2

Prime factorisation of 10 = 2 × 5

Prime factorisation of 20 = 2 × 2 × 5

LCM of 8, 10 and 20 = 2

(c) 15, 35, 45

Solution:

15, 35, 45

Prime factorisation of 15 = 3 × 5

Prime factorisation of 35 = 5 × 7

Prime factorisation of 45 = 3 × 3 × 5

LCM of 15, 35 and 45 = 5

Question 3.

Write all the factors of the following numbers.

(a) 57

Solution:

Factors of 57 = 1 × 3 × 19 × 57

(b) 218

Solution:

Factors of 218 = 1 × 2 × 109 × 218

(c) 100

Solution:

Factors of 100 = 1 × 2 × 5 × 10 × 25 × 50 × 100

(d) 105

Solution:

Factors of 105 = 1 × 3 × 5 × 21 × 35 × 105

Question 4.

Find the HCF of the following:

(a) 15, 36, 50

Solution:

15, 36, 50

Factors of 15 = 1 × 3 × 5 × 15

Factors of 36 = 1 × 2 × 3 × 4 × 9 × 18 × 12 × 36

Factors of 50 = 1 × 2 × 5 × 10 × 25 × 50

Common factors of 15, 36, and 50 = 1

HCF of 15, 36 and 50 = 1

(b) 10, 12, 20

Solution:

10, 12, 20

Factors of 10 = 1 × 2 × 5 × 10

Factors of 12 = 1 × 2 × 3 × 6 × 4 × 12

Factors of 20 = 1 × 2 × 5 × 4 × 10 × 20

Common factors of 10, 12, and 20 = 1, 2

HCF of 10, 12, and 20 = 2

(c) 25, 30, 45

Solution:

25, 30, 45

Factors of 25 = 1 × 5 × 25

Factors of 30 = 1 × 2 × 3 × 5 × 6 × 10 × 15 × 30

Factors of 45 = 1 × 3 × 5 × 9 × 15 × 45

Common factors of 25, 30 and 45 = 1, 5

HCF of 25, 30 and 45 = 5

Question 5.

Circle the composite number.

9, 7, 11, 22, 32, 33, 40, 10, 17, 27, 50, 19, 21, 20, 25, 42, 52, 47

Solution:

9, 22, 32, 33, 40, 10, 27, 50, 21, 20, 25, 42, 52

Question 6.

Using the division method, find the prime factorisation of the following:

(a) 35

Solution:

35

Prime factorisation of 35 = 5 × 7

(b) 21

Solution:

21

Prime factorisation of 21 = 3 × 7

(c) 82

Solution:

82

Prime factorisation of 82 = 2 × 41

(d) 95

Solution:

95

Prime factorisation of 95 = 5 × 19

(e) 56

Solution:

56

Prime factorisation of 56 = 2 × 2 × 2 × 7

Question 7.

Using Factor Tree Method, find the prime factorisation of the following:

(a) 104

Solution:

(b) 96

Solution:

(c) 112

Solution:

(d) 56

Question 8.

Write the prime factorisation of:

(a) 72

Solution:

prime factors of 72 = 2 × 2 × 2 × 3 × 3

(b) 120

Solution:

prime factors of 120 = 2 × 2 × 2 × 3 × 5

(c) 135

Solution:

prime factors of 135 = 3 × 3 × 3 × 5

(d) 145

Solution:

prime factors of 145 = 5 × 29

Question 9.

Find the HCF of the following:

(a) 12, 20, 50

Solution:

2

(b) 24, 72, 90

Solution:

6

(c) 15, 25, 75

Solution:

5

(d) 27, 35, 45

Solution:

1

Question 10.

Circle the prime number in the following group:

10, 15, 19, 7, 21, 11, 13, 5, 3, 79, 19, 37, 51, 29, 17, 37, 41, 53, 57

Solution:

19, 7, 11, 13, 3, 79, 19, 37, 29, 17, 37, 41, 53

Question 11.

Using the Prime Factorisation Method, find the LCM.

(a) 20, 40

Solution:

2 × 2 × 5 × 2 = 40

(b) 9, 16, 48

Solution:

2 × 2 × 3 × 2 × 3 × 2 = 144

(c) 15, 75, 60

Solution:

3 × 5 × 5 × 4 = 300

Question 12.

How many even numbers are there between 30 and 70?

Solution:

18

Question 13.

Fill in the blanks:

Solution:

Question 14.

Using the Division Method, find the prime factorisation of the following:

(a) 105

Solution:

prime factors of 105 = 3 × 5 × 7

(b) 76

Solution:

prime factors of 76 = 2 × 2 × 19

(c) 95

Solution:

prime factors of 95 = 5 × 19

(d) 102

Solution:

prime factors of 102 = 2 × 3 × 17