Find the H.C.F 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

Solution:
(a) Factors of 18 = 2 x 3 x 3 (b) Factors of 30 = 2 x 3 x 5
Factors of 48 = 2 x 2 x 2 x 2 x 3 Factors of 42 = 2 x 3 x 7
H.C.F. (18, 48) = 2 x 3 = 6 H.C.F. (30, 42) = 2 x 3 = 6
(c) Factors of 18 = 2 x 3 x 3 (d) Factors of 27 = 3 x 3 x 3
Factors of 60 = 2 x 2 x 3 x 5 Factors of 63 = 3 x 3 x 7
H.C.F. (18, 60) = 2 x 3 = 6 H.C.F. (27, 63) = 3 x 3 = 9
(e) Factors of 36 = 2 x 2 x 3 x 3 (f) Factors of 34 = 2 x 17
Factors of 84 = 2 x 2 x 3 x 7 Factors of 102 = 2 x 3 x 17
H.C.F. (36, 84) = 2 x 2 x 3 = 12 H.C.F. (34, 102) = 2 x 17 = 34
(g) Factors of 70 = 2 x 5 x 7 (h) Factors of 91 = 7 x 13
Factors of 105 = 3 x 5 x 7 Factors of 112 = 2 x 2 x 2 x 2 x 7
Factors of 175 = 5 x 5 x 7 Factors of 49 = 7 x 7
H.C.F. = 5 x 7 = 35 H.C.F. = 1 x 7 = 7
(i) Factors of 18 = 2 x 3 x 3 (j) Factors of 12 = 2 x 2 x 3
Factors of 54 = 2 x 3 x 3 x 3 Factors of 45 = 3 x 3 x 5
Factors of 81 = 3 x 3 x 3 x 3 Factors of 75 = 3 x 5 x 5
H.C.F. = 3 x 3 = 9 H.C.F. = 1 x 3 = 3

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