Question

Find the HCF of the following by prime factorisation
method:
(i) 38, 361
(ii) 36,72,84
(iii) 75, 25, 120
(iv) 112,140,168
(v) 6,10,14
(vi) 60,72,80​

Answer 1

Answer:

(i) 38, 361

38 = 2 x 19

361 = 19 x 19

HCF = 19 X 1

        = 19

Therefore, HCF of 38 and 361 is 19.

(ii) 36, 72, 84

36 = 2 x 2 x 3 x 3

72 = 2 x 2 x 2 x 3 x 3

84 = 2 x 2 x 3 x 7

HCF = 2 X 2 X 3

        = 12

Therefore. HCF of 36, 72 and 84 is 12.

(iii) 75, 25, 120

75 = 3 x 5 x 5

25 = 5 x 5

120 = 3 x 2 x 2 x 2 x 5

HCF = 5 X 1

        = 5

Therefore, HCF of 75, 25 and 120 is 5

(iv) 112, 140, 168

112 = 2 x 2 x 2 x 2 x 7

140 = 2 x 2 x 5 x 7

168 = 2 x 2 x 2 x 3 x 7

HCF = 2 X 7

        = 14

Therefore, HCF of 112, 140 and 168 is 14.

(v) 6, 10, 14

6 = 2 x 3

10 = 2 x 5

14 = 2 x 7

HCF = 2 X 1

        = 2

Therefore, HCF of 6, 10, 14 is 2.

(vi) 60, 72, 80

60 = 2 x 2 x 3 x 5

72 = 2 x 2 x 2 x 3 x 3

80 = 2 x 2 x 2 x 2 x 5

HCF = 2 X 2

        = 4

Therefore, HCF of 60, 72 and 80 is 4.