Q. 14.7( 52 Votes )

# 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

Answer :

HCF – Highest common factor

The highest common factor of two or more numbers is the largest number that divides saparetly both the numbers.

**(a)** 18 and 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

Rate this question :

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

NCERT - MathematicsThe HCF of two or more given numbers is the highest of their common_____.

NCERT - Exemplar MathematicsThe HCF of two numbers is smaller than the smaller of the numbers.

HCF of two or more numbers may be one of the numbers.