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
Using prime factorization we have, 


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


30 = 2 × 3 × 5

42 = 2 × 3 × 7

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

(c) 18, 60


18 = 2 × 3 × 3

60 = 2 × 2 × 3 × 5

HCF = 2 × 3 = 6

Therefore the HCF of 18, 60 is 6.

(d) 27, 63

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

(e) 36, 84

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