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**Number Line Prime Class 6 Solutions Chapter 5 Playing with Numbers**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Number Line Prime Class 6 Math Book, Chapter 5, Playing with Numbers. Here students can easily find step by step solutions of all the problems for Playing with Numbers, Exercise 5A, 5B, 5C, 5D, 5E and 5F Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 5 solutions. Here in this post all the solutions are based on latest Syllabus.

**Playing with Numbers Exercise 5A Solution :**

**Question number – (1)**

**Solution :**

= 18 + 9 – 15 + 3

= 18 + 9 +3 – 15

= 30 – 15

= 15

**Question number – (2)**

**Solution :**

= 27 ÷ 3 × 4 – 5

= 9 × 4 – 5

= 36 – 5

= 31

**Question number – (3)**

**Solution :**

= 900 + 2000 ÷ 500 × 6

= 900 + 4 × 6

= 900 + 24

= 924

**Question number – (4)**

**Solution :**

= 35 + 12 – 4 × 8 ÷ 2

= 47 – 4 × 4

= 47 – 16

= 31

**Question number – (5)**

**Solution :**

= 25 × 5 – 12 + 18 ÷ 9

= 125 – 12 + 2

= 125 – 10

= 115

**Question number – (6)**

**Solution :**

= 45678 – 3124 + 5670

= 45678 + 5670 + 3124

= 51348 – 3124

= 48,224

**Question number – (7)**

**Solution :**

= 881 × 2 + 24 – 12 ÷ 2

= 1762 + 24 – 6

= 1786 – 6

= 1780

**Question number – (8)**

**Solution :**

= 65 ÷ 5 × 3 + 17 – 5

= 13 × 3 + 17 – 5

= 39 + 17 – 5

= 56 – 5

= 51

**Question number – (9)**

**Solution :**

= 124 × 13 + 16 ÷ 4

= 1612 + 4

= 1616

**Question number – (10)**

**Solution :**

= 18 + 10 – 7 × 32 ÷ 1/3 of 24

= 18 + 10 – 7 × 32 ÷ 1/3 × 24

= 18 + 10 – 7 × 32 ÷ 8

= 28 – 7 × 4

= 28 – 28

= 0

**Question number – (11)**

**Solution :**

= 9 of 12 – 16 + 32 × 2

= 9 × 12 – 16 + 32 × 2

= 108 + 64 – 16

= 172 – 16

= 156

**Question number – (12)**

**Solution :**

= 42 ÷ 7 × 3 + 1/6 of 54 × 5

= 42 ÷ 7 × 3 + 1/6 × 54 × 5

= 6 × 3 + 9 × 5

= 18 + 45

= 63

**Playing with Numbers Exercise 5B Solution :**

**Question no – (1) **

**Solution :**

**(a)** [7 ÷ (12 – 5)

**(b)** [(9 + 4) × 6]

**(c)** [(13 + 12 – (9 – 2)

**(d)** [(5 × 2) + (18 – 15)]

**Question no –** **(2) **

**Solution :**

**(a) 42 – [20 – {19 – (14 – 8 – 4}]**

= 42 – [20 – {19 – (14 – 12}]

= 42 – [20 – {19 – 2}]

= 42 – [20 – 17]

= 42 – 3

= 39

**(b) 910 – [80 {24 – (77 – 50}]**

= 910 – [80 + {34 – 27}]

= 910 – [80 + 7]

= 910 – 87

= 823

**(c) 54 + 9 (43 – 26 – 2) ÷ 3**

= 54 + 9 (43 – 28) ÷ 3

= 54 + 9 × 15 ÷ 3

= 54 + 135 ÷ 3

= 54 + 45

= 99

**(d) 555 + {22 + 343 – (16 ÷ 8 + 13 – 15)}**

= 555 + {22 + 343 – (2 + 13 – 15)}

= 555 + {22 + 343 – (15 – 15)

= 555 + 22 + 343

= 920

**(e) 91 – [22 – {16 ÷ (39 + 30 of 3 – 40)}]**

= 91 – [22 – {16 ÷ 93 + 3 × 3 – 40)}]

= 91 – [22 – {16 ÷ (39 + 9 – 40)}]

= 91 – [22 – {16 ÷ (48 – 40)}]

= 91 – [22 – {16 ÷ 8}]

= 91 – [22 – 2]

= 91 – 20

= 71

**(f) 27 + 3 – [29 – {6 ÷ 3 – (5 – 6 ÷ 3) ÷ 3}]**

= 30 – [29 – {6 ÷ 3 – (5 – 2) ÷ 3]

= 30 – [29 – {2 – 1}

= 30 – [29 – 1]

= 30 – 28

= 2

**Playing with Numbers Exercise 5C Solution :**

**Question number – (1)**

**Solution :**

= (2, 4), (4, 6), (6, 8), (8, 10), (10, 12), (12, 14), (14, 16), (16, 20), (22, 24), (26, 28)

**Question number – (2)**

**Solution :**

Prime numbers are

= 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79

**Question number – (3)**

**Solution :**

= Co-prime number

= (8, 15), (7, 13), (11, 17), (6, 11)

**Question number – (4)**

**Solution :**

Twin prime number –

= (3, 5), (5, 7), (7, 11), (11, 13)

**Question number – (5)**

**Solution :**

Yes, composite number can be odd

smallest odd composite number is 9

**Question no – (6)**

**Solution :**

(a) 37 + 5 + 3

(b) 7 + 3 + 2

(c) 7 + 5 + 3

(d) 13 + 5 + 3

**Question no – (7) **

**Solution :**

**(a)** 1, 3, 5, 15, 25, 75

**(b)** 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 96

**(c)** 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

**(d)** 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 100

**Question** no – (8)

**Solution :**

**(a)** (2 × 2 × 2 × 2 × 5) + 1

**(b)** (2 × 2 × 2 × 5 × 13) + 1

**(c)** (2 × 3 × 3 × 5) + 1

**Question** no – (9)

**Solution :**

Multiples of both 4 and 6 are –

= 12, 24, 36, 48, 60

**Question**** no – (10) **

**Solution :**

**(a)** 2 × 13 × 7

**(b)** 2 × 5 × 5 × 17

**(c)** 2 × 2 × 3 × 5 × 7

**(d)** 5 × 2 × 2 73

**(e)** 2 × 2 × 7 × 7 × 13

**(f)** 5 × 2 × 2 × 2 × 37

**Playing with Numbers Exercise 5D Solution :**

**Question no – (1)**

**Solution :**

**(a)** Is not divisible by 8

As last three digit is not divisible by 8

**(b)** Is divisible by 8

As last there digit is divisible by 8

**(c)** Is not divisible by 8

As formed digit by last time digit is not divisible by 8

**(d)** Is divisible by 8

**Question no – (2) **

**Solution :**

**(a)** is divisible by 5 but not by 10

**(b)** is divisible by both 5 and 10

**(c)** is divisible by both 5 and 10

(**d**) is divisible by 5 but not by 10

**Question number – (3)**

**Solution :**

**(a)** is divisible by 6 but not by 12 and 15

**(b)** is divisible by 6 and 12 but not by 15

**(c)** by 6, 12 and 15

**(d)** is not divisible by 6, 12 not 15

**Question number – (4)**

**Solution :**

**(a)** 489** 2**76

**(b)** 3** 5**541

**(c)** 9987** 5**7

**(d)** 242** 0**73

Now sum of all digit can be divisible by 9

So, the number is also divisible by 9

**Question number – (5)**

**Solution :**

**(a)** 3856__8__

**(b)** 6** 1**566

**(c)** 2456** 2**89

**(d)** 26262__0__

**Question no – (7) **

**Solution :**

**(a)** Divisible by 3 not by 6 –

= 21, 27

**(b)** Divisible by 12 not by 15 –

= 36, 72

**(c)** Divisible by 2 not by 8 –

= 18, 14

**(d)** Divisible by 5 not by 10 –

= 105, 115

**Playing with Numbers Exercise 5E Solution :**

**Question no – (1) **

**Solution :**

HCF by prime factorization number

**(a) 324 and 1224**

324 = 2 × 2 × 3 × 3 × 3 × 3

1224 = 2 × 2 × 2 × 3 × 3 × 7

**∴** HCF = 2 × 2 × 3 × 3

= 36

**(b) 578 and 2200**

578 = 2 × 17 × 17

2200 = 2 × 2 × 2 × 275

**∴** HCF = 2

**(c) 82 and 196**

82 = 2 × 1 × 41

196 = 2 × 2 × 49

**∴** HCF = 2

**(d) 42, 56 and 105**

42 = 2 × 3 × 7

56 = 2 × 2 × 2 × 7

105 = 3 × 5 × 7

**∴** HCF = 7

**Question no – (2) **

**Solution :**

**(a) 144 and 180**

**∴** HCF = 36

**(b) 2820 and 4884**

**∴** HCF = 12

**(c) 256 and 386**

**∴** HCF = 2

**(d) 154, 1174 and 2066**

**∴** HCF = 2

**Question no – (3)**

**Solution :**

Blue marbles = 18

White marbles = 24

So, Greatest number of column Ankit can make is 6.

**Question no – (4)**

**Solution :**

So, Maximum number of heaps possible is 4.

**Question no – (5)**

**Solution :**

The numbers are –> 35, 62 and 85

And remainders are -> 8, 8 and 4

So, the numbers are –

(35 – 8)

= 27

= 3 × 3 × 3

(62 – 8)

= 54

= 2 × 3 × 3 × 3

(85 – 4)

= 81

= 3 × 3 × 3 × 3

**∴** The greatest number is 27

**Playing with Numbers Exercise 5F Solution :**

**Question no – (1) **

**Solution :**

**(a) 84 and 156 **

LCM = 2 × 2 × 3 × 7 × 13

= 1092

**(b) 324 and 486 **

LCM = 2 × 3 × 3 × 9 × 2 × 3

= 972

**(c) 48, 96 and 120**

LCM = 2 × 2 × 3 × 2 × 2 × 1 × 2 × 5

= 480

**Question no – (2)**

**Solution :**

**(a) 28 and 86**

LCM = 2 × 1 × 14 × 43

= 1204

**(b) 51, 17 and 39**

LCM = 3 × 17 × 13

= 663

**(c) 19, 76, 152 and 228 **

LCM = 4 × 19 × 2 × 3

= 456

**Question no – (3)**

**Solution :**

We know product of two number = HCF × LCM

So, 460 × 232

= 4 × LCM

=> LCM = 450 × 232/4

= 26,680

**Question no – (4)**

**Solution :**

Same

540 × 940

= HCF × LCM

=> HCF × 3780

= 540 × 945

=> HCF = 540 × 945/3780

= 135

**Question no – (5)**

**Solution :**

Other number × 265 = 5 × 46,905

=> Other number

= 5 × 46,905/265

= 885

**Question no – (6)**

**Solution :**

HCF of two co-prime number = 1

So, 1 × 153

= 17 × other number

=> Other number

= 153/17

= 9

**Question no – (7)**

**Solution :**

LCM = 5 × 37 × 70

= 12,950

**∴** So, HCF = 5

**Chapter 5 Review Time Questions Solution : **

**Question no – (1)**

**Solution :**

The correct option is – (a) Odd

**Question no – (2)**

**Solution :**

The correct option is – (a) Even

**Question no – (3) **

**Solution :**

The correct option is – (b) 2

**Question no – (4) **

**Solution :**

The correct option is – (b) 1, 2, 3, 6

**Question no – (5) **

**Solution :**

The correct option is – (d) 8

**Question no – (6)**

**Solution :**

The correct option is – (a) 1111

**Question no – (7)**

**Solution :**

The correct option is – (b) 900

**Question no – (8)**

**Solution :**

The correct option is – (c) Co-prime numbers

**Question no – (9)**

**Solution :**

The correct option is – (c) The number formed by its last three digit is divisible by 8

**Question no – (10) **

**Solution :**

The correct option is – (b) 2

**Next Chapter Solution : **

👉 Chapter 6 👈