Question

Find the HCF of the following numbers by using prime factorization method: (i) 18, 60 (ii) 27, 63 (iii) 70, 105, 175 (iv) 18, 54, 81 (v) 12, 45, 75​

Answer 1

Answer:

i) 6

ii) 9

ii) 35

iv) 9

v) 3

Step-by-step explanation:

i) HCF of 18 and 60

18 = 2 X 3 X 3

60 = 2X 2X 3 X 5

We can see that 2 and 3 are common in both.

∴ HCF of 18 & 60 = 2 X 3

∴ HCF = 6

ii) HCF of 27 and 63

27 = 3 X 3 X 3

63 = 3 X 3 X 7

We can see that 3 is common and there are 2 common 3's.

∴ HCF of 27 & 63 = 3 X 3

∴ HCF = 9

iii) HCF of 70, 105 and 175

70 = 2 X 5 X 7

105 = 3 X 5 X 7

175 = 5 X 5 X 7

We can see that 5 and 7 are common

∴ HCF = 5 X 7

∴ HCF = 35

iv) 18, 54 and 81

18 = 2 X 3 X 3

54 = 2 X 3 X 3 X3

81 = 3 X 3 X 3 X 3

We can see that 3 is common and there are 2 common 3's.

∴ HCF = 3 X 3

∴ HCF = 9

v) 12, 45 and 75

12 = 2 X 2 X 3

45 = 3 X 3 X 5

75 = 3 X 5 X 5

We can see that 3 is the only common number

∴ HCF = 3

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