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