Punjab State Board PSEB 6th Class Maths Book Solutions Chapter 3 Playing with Numbers Ex 3.1 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 6 Maths Chapter 3 Playing with Numbers Ex 3.1

1. Write down all the factors of each of the following:

Question (i)

18

Solution:

18 = 1 × 18

18 = 2 × 9

18 = 3 × 6

So, 1, 2, 3, 6, 9 and 18 are factors of 18

Question (ii)

24

Solution:

24 = 1 × 24

24 = 2 × 12

24 = 3 × 8

24 = 4 × 6

So, 1, 2, 3, 4, 6, 8, 12 and 24 are factors of 24

Question (iii)

45

Solution:

45 = 1 × 45

45 = 3 × 15

45 = 5 × 9

So, 1, 3, 5, 9, 15 and 45 are factors of 45

Question (iv)

60

Solution:

60 = 1 × 60

60 = 2 × 30

60 = 3 × 20

60 = 4 × 15

60 = 5 × 12

60 = 6 × 10

So, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60

Question (v)

65.

Solution:

65 = 1 × 65

65 = 5 × 13

So, 1, 5, 13 and 65 are the factors of 65

2. Write down the first six multiples of each of the following:

Question (i)

6

Solution:

First six multiples of 6 are:

6, 12, 18, 24, 30 and 36

Question (ii)

9

Solution:

First six multiples of 9 are:

9, 18, 27, 36, 45 and 54

Question (iii)

11

Solution:

First six multiples of 11 are:

11, 22, 33, 44, 55 and 66

Question (iv)

15

Solution:

First six multiples of 15 are:

15, 30, 45, 60, 75 and 90

Question (v)

24.

Solution:

First six multiples of 24 are:

24, 48, 72, 96, 120 and 144

3. List all the numbers less than 100 that are multiples of:

Question (i)

17

Solution:

Multiples of 17 less than 100 are:

17, 34, 51, 68 and 85

Question (ii)

12

Solution:

Multiples of 12 less than 100 are:

12, 24, 36,48, 60, 72, 84 and 96

Question (iii)

21.

Solution:

Multiples of 21 less than 100 are:

21, 42, 63 and 84

4. Which of the following are prime numbers?

Question (i)

39

Solution:

Given number = 39

We find that 39 is divisible by 3.

∴ It has more than two factors.

∴ So, 39 is not a prime number

Question (ii)

129

Solution:

Given number =129

It is divisible by 1 and itself So, it has exactly two factors.

∴ 129 is a prime number

Question (iii)

177

Solution:

Given number = 177

We find that 177 is divisble by 3

∴ It has more than two factors.

So, 177 is not a prime number

Question (iv)

203

Solution:

Given number = 203

It is divisible by 1 and itself

So, 203 is a prime number

Question (v)

237

Solution:

Given number = 237

We find that 237 is divisible by 3

∴ It has more than two factors.

So, 237 is not a prime number

Question (vi)

361.

Solution:

Given number = 361

We find that 361 is divisible by 19

∴ It has more than two factors.

So, 361 is not a prime number

5. Express each of the following as sum of two odd prime numbers:

Question (i)

16

Solution:

16 = 3 + 13

= 5 + 11

Question (ii)

28

Solution:

28 = 11+ 17

Question (iii)

40.

Solution:

40 = 3 + 37

= 11 + 29

= 17 + 23

6. Write all the prime numbers between the given numbers:

Question (i)

1 to 25

Solution:

Prime numbers between 1 to 25 are:

2, 3, 5, 7, 11, 13, 17, 19, 23

Question (ii)

85 to 105

Solution:

Prime numbers between 85 to 105 are:

89, 97, 101, 103

Question (iii)

120 to 140.

Solution:

Prime numbers between 120 to 140 are:

127, 129, 131, 137, 139

7. Is 36 a perfect number?

Solution:

Factors of 36 are:

2, 3, 4, 6, 9, 12, 18, 36

Sum of all the factors of 36

= 2 + 3 + 4 + 6 + 9 + 12+18 + 36

= 90

= 2 × 45

But sum of all factors of a number = 2 × Number

Thus, 36 is not a perfect number

8. Find the missing factors:

Question (i)

(i) 5 × …. = 30

(ii) …. × 6 = 48

(iii) 7 × …. = 63

(iv) …. × 8 = 104

(v) …. × 7 = 105.

Solution:

(i) 5 × 6 =30

(ii) 8 × 6 = 48

(iii) 7 × 9 = 63

(iv) 13 × 8 = 104

(v) 15 × 7 = 105.

9. List all 2-digit prime numbers, in which both the digits are prime numbers.

Solution:

All 2-digit numbers, in which both the digits are prime numbers are:

23, 37, 53, 73