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Learn Exercise 3.6 with Free Lessons & Tips

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

(a) 18, 48

18 = 2 × 3 × 3

48 = 2 × 2 × 2 × 2 × 3

HCF = 2 × 3 = 6

(b) 30, 42

30 = 2 × 3 × 5

42 = 2 × 3 × 7

HCF = 2 × 3 = 6

(c) 18, 60

18 = 2 × 3 × 3

60 = 2 × 2 × 3 × 5

HCF = 2 × 3 = 6

(d) 27, 63

27 = 3 × 3 × 3

63 = 3 × 3 × 7

HCF = 3 × 3 = 9

(e) 36, 84

36 = 2 × 2 × 3 × 3

84 = 2 × 2 × 3 × 7

HCF = 2 × 2 × 3 = 12

(f) 34, 102

34 = 2 × 17

102 = 2 × 3 × 17

HCF = 2 ×17 = 34

(g) 70, 105, 175

70 = 2 × 5 × 7

105 = 3 × 5 × 7

175 = 5 × 5 × 7

HCF = 5 × 7 = 35

(h) 91, 112, 49

91 = 7 × 13

112 = 2 × 2 × 2 × 2 × 7

49 = 7 × 7

HCF = 7

(i) 18, 54, 81

18 = 2 × 3 × 3

54 = 2 × 3 × 3 × 3

81 = 3 × 3 × 3 × 3

HCF = 3 × 3 = 9

(j) 12, 45, 75

12 = 2 ×2 × 3

45 = 3 × 3 × 5

75 = 3 × 5 × 5

HCF = 3

Comments

What is the HCF of two consecutive

(a) Numbers? (b) Even numbers? (c) Odd numbers?

(i) 1 e.g., HCF of 2 and 3 is 1.

(ii) 2 e.g., HCF of 2 and 4 is 2.

(iii) 1 e.g., HCF of 3 and 5 is 1.

Comments

HCF of co-prime numbers 4 and 15 was found as follows by factorization:

4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factors, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?

No. The answer is not correct. 1 is the correct HCF.

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