Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12

Maharashtra State Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12

Question 1.
i. 25, 40
ii. 56, 32
iii. 40, 60, 75
iv. 16, 27
v. 18, 32,48
vi. 105, 154
vii. 42, 45, 48
viii. 57, 75, 102
ix. 56, 57
x. 777, 315, 588
Solution:
i. 25, 40
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 1
∴ 25 = 5 × 5
40 = 2 × 2 × 2 × 5
∴ HCF of 25 and 40 = 5

ii. 56, 32
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 2
∴ 56 = 2 × 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
∴ HCF of 56 and 32 = 2 × 2 × 2
∴ HCF of 56 and 32 = 8

iii. 40, 60, 75
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 3
∴ 40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
∴ HCF of 40, 60 and 75 = 5

iv. 16, 27
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 4
∴ 16 = 2 × 2 × 2 × 2 × 1
27 = 3 × 3 × 3 × 1
∴ HCF of 16 and 27 = 1

v. 18, 32,48
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 5
∴ 18 = 2 × 3 × 3
32 = 2 × 2 × 2 × 2 × 2
48 = 2 × 2 × 2 × 2 × 3
∴ HCF of 18, 32 and 48 = 2

vi. 105, 154
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 6
∴ 105 = 3 × 5 × 7
154 = 2 × 2 × 11
∴ HCF of 105 and 154 = 7

vii. 42, 45, 48
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 7
∴ 42 = 2 × 3 × 7
45 = 3 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3
∴ HCF of 42,45 and 48 =3

viii. 57, 75, 102
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 8
∴ 57 = 3 × 19
75 = 3 × 5 × 5
102 = 2 × 3 × 17
∴ HCF of 57, 75 and 102 = 3

ix. 56, 57
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 9
∴ 56 = 2 × 2 × 2 × 7 × 1
57 = 3 × 19 × 1
∴ HCF of 56 and 57 = 1

x. 777, 315, 588
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 10
∴ 777 = 3 × 7 × 37
315 = 3 × 3 × 5 × 7
588 = 2 × 2 × 3 × 7 × 7
∴ HCF of 777, 315 and 588 = 3 × 7
HCF of 777, 315 and 588 = 21

Question 2.
Find the HCF by the division method and reduce to the simplest form:
i. \(\frac { 275 }{ 525 }\)
ii. \(\frac { 76 }{ 133 }\)
iii. \(\frac { 161 }{ 69 }\)
Solution:
i. \(\frac { 275 }{ 525 }\)
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 11

ii. \(\frac { 76 }{ 133 }\)
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 12

iii. \(\frac { 161 }{ 69 }\)
Maharashtra Board Class 7 Maths Solutions Chapter 3 HCF and LCM Practice Set 12 13

Maharashtra Board Class 7 Maths Chapter 3 HCF and LCM Practice Set 12 Intext Questions and Activities

Question 1.
In each of the following examples, write all the factors of the numbers and find the greatest common divisor. (Textbook pg. no. 17)
i. 28, 42
ii. 51, 27
iii. 25, 15, 35
Solution:
i. Factors of 28 = 1,2,4, 7, 14, 28
Factors of 42 = 1,2, 3, 6, 7, 14, 21, 42
∴ HCF of 28 and 42 = 14

ii. Factors of 51 = 1, 3, 17, 51
Factors of 27 = 1, 3, 9, 27
∴ HCF of 51 and 27 = 3

iii. Factors of 25 = 1, 5, 25
Factors of 15 = 1, 3, 5, 15
Factors of 35 = 1, 5, 7, 35
∴ HCF of 25, 15 and 35 = 5

Maharashtra Board Class 7 Maths Solutions

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