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**Joy of Mathematics Class 6 Solutions Chapter 4 Factors and Multiples**

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Joy of Mathematics Class 6 Book, Chapter 4 Factors and Multiples. Here students can easily find step by step solutions of all the problems for Factors and Multiples. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Students will get chapter 4 solutions. Here students will find exercise wise solutions for chapter 4 Exercise 4.1, 4.2, 4.3, 4.4 and 4.5

**Factors and Multiples Exercise 4.1 Solution :**

**Question no – (1)**

**Solution :**

**(a)** Factors are = 1, 13

**(b)** Factors are = 1, 3, 9, 27

**(c)** Factors are = 1, 5, 7, 35

**(d)** Factors are = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

**(e)** Factors are = 1, 2, 4, 8, 16, 32, 64

**(f)** Factors are = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

**(g)** Factors are = 1, 3, 5, 7, 15, 21, 35, 105

**(h)** Factors are = 1, 5, 7, 25, 35, 175

**Question no – (2) **

**Solution :**

**(a)** Six multiples 4 are = 4, 8, 12, 16, 20, 24

**(b)** Six multiples 5 are = 5, 10, 15, 20, 25, 30

**(c)** Six multiples 6 are = 6, 12, 18, 24, 30, 36

**(d)** Six multiples 8 are = 8, 16, 24, 32, 40, 48

**(e)** Six multiples 11 are = 11, 22, 33, 44, 55, 66

**(f)** Six multiples 12 are = 12, 24, 36, 48, 60, 72

**(g)** Six multiples 13 are = 13, 26, 39, 52, 65, 78

**(h)** Six multiples 16 are = 16, 32, 48, 64, 80, 96

**Question no – (3) **

**Solution :**

**(a) Factor 19**

= 1 × 19

**∴** 99541 is divisible by 19.

So, the number is 99541.

**Question no – (4)**

**Solution :**

Multiplies of 5 less than 100 are

= 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95

**Question no – (5)**

**Solution :**

14^{th} and 18^{th} multiples of 16 is

= 16 × 14 = 224

= 16 × 18 = 288

**Question no – (6)**

**Solution :**

Multiplies of 15 less than 100 are 15, 30, 45, 60, 75, 90

**Question no – (7)**

**Solution :**

19038 = 19000 + 38

= 19 (1000 + 2)

Therefore, 19 is a factor of 19038

**Factors and Multiples Exercise 4.2 Solution :**

**Question no – (1) **

**Solution :**

**(a)** All prime numbers,

= 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

**(b)** All prime numbers are,

= 31, 37, 41, 43, 47

**(c)** All prime numbers are,

= 101, 103, 107, 109, 113, 127, 131, 137, 139, 149

**(d)** All prime numbers are,

= 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

**Question no – (2) **

**Solution :**

**(a)** 37 = Prime no (1, 37)

**(b)** 39 = Composite no (1, 3, 39)

**(c)** 59 = Prime no (1, 59)

**(d)** 91 = Composite no (1, 91, 3, 17)

**(e)** 99 = Composite no (1, 3, 99)

**(f)** 103 = Prime no

**Question no – (3) **

**Solution :**

**(a)** Composite numbers are = 10, 12, 14, 15, 16, 18

**(b)** Composite numbers are = 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50

**(c)** Composite numbers are = 62, 63, 64, 65, 66, 68, 69

**(d)** Composite numbers are = 91, 92, 93, 94, 95, 96

**Question no – (4)**

**Solution :**

The formed number will be Composite number.

**Question no – (5)**

**Solution :**

The required numbers are,

Twin prime (3, 5), (5, 7), (11, 13)

Co-prime (4, 9), (5, 7), (11, 17)

**Question no – (6)**

**Solution :**

Possible digit are, = (1, 3, 7, 9)

**Question no – (7)**

**Solution :**

Twin prime = (41, 43), (71, 73)

Co-prime = (41, 43), (45, 47), (49, 51), (51, 53), (53, 55), (55, 57)

**Question no – (8) **

**Solution :**

**(a)** (**29**, 31)

**(b)** (41, **43**)

**(c)** (71, **73**)

**(d)** (101, **103**)

**Question no – (9)**

**Solution :**

The numbers are,

= (23, 37, 53, 73)

**Question no – (10)**

**Solution :**

The three prime numbers are, where sum is 30,

= (2, 5, 23), (2, 11, 17)

**Factors and Multiples Exercise 4.4 Solution :**

**Question no – (1) **

**Solution :**

**(a) 20 = 1, 2, 4, 5**

28 = 1, 2, 4, 7

**∴** Common factor = (1, 2, 4)

**(b) 42 = 1, 2, 3, 6, 7**

60 = 1, 2, 3, 4, 5, 6, 12

**∴** Common factor = (1, 2, 3, 6)

**(c) 63 = 1, 3, 7, 9, 63**

91 = 1, 7, 13, 31

**∴** C.F. = (1, 7)

**(d) 120, 160**

**∴ **Common factor = (1, 2, 3, 4, 6, 8, 12, 24)

**Question no – (2) **

**Solution :**

**(a) 646**

**∴** Prime factors

= (2 × 17 × 19)

**(b) 848**

**∴** Factors

= (2 × 2 × 2 × 2 × 58)

**(c) 945**

**∴** Factors are

= (3 × 3 × 3 × 5 × 7)

**(d) 1226**

**∴** Factors are

= (2 × 613)

**(e) 1035**

**∴** Factors are,

= (5 × 3 × 3 × 23)

**Question no – (3)**

**Solution : **

**(a) P _{54} and P**

_{66 }54 = 2 × 3 × 3 × 3

66 = 2 × 3 × 11

**∴ **Common factor is = (2, 3)

**(b)** Set of all factors are = (2, 3, 11)

**Question no – (4)**

**Solution :**

**F _{48} and F_{60}**

_{}

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factor of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

**∴** Largest element common factor = 12

**Question no – (5) **

**Solution :**

**(a) 144 and 18**

**∴** 144 = 2 × 2 × 2 × 3 × 2 × 3

180 = 2 × 2 × 3 × 3 × 5

**∴** H.C.F is = 2 × 2 × 3 = 12

**(b) 120 and 204**

**∴** 120 = 2 × 2 × 2 × 3 × 5

204 = 2 × 2 × 3 × 17

**∴** H.C.F. is = (2 × 2 × 3)

= 12

**(c) 72 and 108**

**∴** 72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

**∴** H.C.F. is = (2 × 2 × 3 × 3)

= 36

**(d) 44 and 110**

**∴** 44 = 2 × 2 × 11

110 = 2 × 5 × 11

**∴** H.C.F. is = 2 × 11

= 22

**Question no – (6) **

**Solution : **

**(a) 615, 1599**

**∴ **H.C.F. is = 123

**(b) 219, 1022**

**∴** H.C.F. is = 73

**(c) 882, 3150**

**∴** H.C.F. is 126

**(d) 513, 6384**

**∴** H.C.F. is 57

**Question no – (7)**

**Solution :**

The H.C.F of any two consecutive odd numbers is 1

**Question no – (8)**

**Solution :**

**∴** H.C.F. is 12

**Question no – (9)**

**Solution :**

Here, 285 – 9 = 276

1249 – 7 = 1242

**∴ **The greatest no is 138

**Question no – (10)**

**Solution :**

Here, 2273 – 5 = 22.68

1823 – 5 = 1818

977 – 5 = 972

**∴** Greatest number is 18

**Question no – (11)**

**Solution : **

Here, 445 – 4 = 441

572 – 5 = 567

699 – 6 = 693

Now,

**∴ **Greatest no is 63

**Question no – (12)**

**Solution :**

Length = 21m 36cm = 2136cm

Broad = 17m 4cm = 1704cm

Area = 3639744cm^{2}

**Question no – (13)**

**Solution :**

Taking H.C.F.

**∴ **H.C.F is 24

Number of square shaped PLACE

= 120 × 96/24 × 24

= 20

**Question no – (14)**

**Solution :**

Taking H.C.F.

**∴** HCF is 525 cm

**∴** Maximum length of take 525 cm.

**Factors and Multiples Exercise 4.5 Solution :**

**Question no – (1) **

**Solution :**

**(a)** M16 multiples = 16, 32, 48, 64, 80, 96, 102, 128, 144, 160, 176, 192,..…..

M20 multiples = 20, 40, 60, 60, 100, 120, 140, 160, 180, 200,……..

**∴** (80, 160,…….)

**(b)** Multiple of M25 = 25, 50, 75, 100, 128, 150, 175, 200, 225, 250, 275,….,400,…….

Multiple of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400,……

**∴** (200, 400, 600,…..)

**Question no – (2) **

**Solutions :**

**(a) 9, 21**

9 = 9, 18, 27, 36, 45, 54, 63,…..

21 = 21, 42, 63, 84, 105,…..

**∴** L.C.M. is 63

**(b) 16, 36**

16 = 16, 32, 48, 64, 80, 96, 102, 128, 144, 160

36 = 36, 72, 108, 144, 180,…..

**∴** L.C.M. is = 144

**(c) 22, 42**

22 = 22, 44, 66, 88, 110, 132, 154,…..

42 = 42, 84, 126, 168, 210

**∴** L.C.M. is = (2 × 11 × 21)

= (22 × 21)

= 462

**Question no – (3) **

**Solutions :**

**(a) 9, 18**

**∴** L.C.M. is = (3 × 3 × 2)

= 18

**(b) 64, 128**

**∴** L.C.M. is = (2 × 2 × 2 × 2 × 2 × 2 × 2)

= 128

**(c) 9, 24, 36**

**∴** L.C.M. is = (3 × 2 × 2 × 3 × 2)

= 72

**(d) 6, 8, 45**

**∴** L.C.M. is = (3 × 2 × 4 × 15)

= 360

**(e) 15, 35, 45**

**∴** L.C.M. is = 5 × 3 × 7 × 3

= 315

**(f) 64, 72, 96, 192**

**∴** L.C.M. is 576

**(4) Find the LCM of the following by division method**

**Solutions :**

**(a) 48, 72, 80**

L.C.M. = (3 × 2 × 2 × 2 × 2 × 3 × 5)

= 720

**(b) 40, 48, 90**

**∴** L.C.M. = 720

**(c) 32, 48, 60, 72**

**∴** L.C.M. = (2 × 2 × 2 × 2 × 3 × 2 × 5 × 3)

= 1440

**(d) 32, 56, 80, 154**

**∴** L.C.M. = (2 × 2 × 7 × 2 × 2 × 2 × 5 × 11)

= 12320

**(e) 224, 280, 236**

**∴** L.C.M. = 66080

**Question no – (5)**

**Solution :**

Other number,

= 131 × 8253/917

= 1179

**Question no – (6)**

**Solution :**

Other number,

= 23 × 1449/161

= 207

**Question no – (7)**

**Solution :**

L.C.M. is = 2160/12

= 180

**Question no – (8)**

**Solution :**

No, the product of three no is not equal to the product of their HCF and LCM.

**Question no – (9)**

**Solution :**

HCF is = 5

LCM is = 360

Multiple of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360,…. minutes

Multiple of 45 = 45, 90, 135, 180, 225, 270, 315, 360 minutes

**∴** L.C.M. = 360 minutes

= 6 hours

**∴** (10.15 AM + 6hour) = 4.15pm

**Question no – (10)**

**Solution :**

L.C.M. = 120 second = 2 minute

In 30 minutes = 30/2

= 15 times

**Question no – (11)**

**Solution :**

Ajay save 9.25 Rs daily.

So, for exact no of Rs.

= (4 × 9)

= 36 Rs

and (4 × 0.25)

= 1 Rs

**∴** (36 + 1)

= 37 Rs in 4 days.

**Next Chapter Solution : **

👉 Chapter 5 👈