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Find the HCF of the following numbers :
(a) 18, 48 (b) 30, 42 (c) 18, 60 (d) 27, 63 (e) 36, 84
(f) 34, 102 (g) 70, 105, 175 (h) 91, 112, 49 (i) 18, 54, 81 (j) 12, 45, 75

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Detailed Solution

(a) 18, 48
Using prime factorization we have,
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 1
Question Image
18 = 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

HCF = 2 × 3 = 6
Therefore the HCF of 18, 48 is 6.

(b) 30, 42
NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 3

30 = 2 × 3 × 5

42 = 2 × 3 × 7

HCF = 2 × 3 = 6
Therefore the HCF of 30, 42 is 6.

60 = 2 × 2 × 3 × 5

HCF = 2 × 3 = 6

Therefore the HCF of 18, 60 is 6.

(d) 27, 63

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 7

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 8

27 = 3 × 3 × 3
63 = 3 × 3 × 7
HCF = 3 × 3 = 9
Therefore the HCF of 27, 63 is 9.

(e) 36, 84

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 9

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.6 - 10

36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
HCF = 2 × 2 × 3 = 12
Therefore the HCF of 36, 84 is 12.

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