Question

Use a method of your own choice to find the H.C.F. of :

(i) 45, 75 and 135

(ii) 48, 36 and 96

(iii) 66, 33 and 132

(iv) 24, 36, 60 and 132

(v) 30, 60, 90 and 105

Answer 1

(i) Factor of 45 = F₄₅ = 3 x 3 x 5

Factor of 75 = F₇₅ = 3 x 5 x 5

and Factor of 135 = F₁₃₅ = 3 x 3 x 3 x 5

Now the common factors of 45, 75 and 135 = 3 and 5

H.C.F. = 3 x 5 = 15

(ii) Factor of 48 = F₄₈ = 2 x 2 x 2 x 2 x 3

Factor of 36 = F₃₆ = 2 x 2 x 3 x 3

and factor of 96 = 2 x 2 x 2 x 2 x 2 x 3

Now the common factor of 48, 36 and 96 = 2, 2 and 3

H.C.F. = 2 x 2 x 3 = 12

(iii) Factor of 66 = F₆₆ = 2 x 3 x 11

Factor of 33 = F₃₃ = 3 x 11

and factor of 132 = F₁₃₂ = 2 x 2 x 3 x 11

Now the common factor of 66, 33 and 132 = 3 and 11

H.C.F. = 3 x 11 =33

(iv) Factor of 24 = F₂₄ = 2 x 2 x 2 x 3

Factor of 36 = F₃₆ = 2 x 2 x 3 x 3

Factor of 60 = F₆₀ = 2 x 2 x 3 x 5

and Factor of 132 = F₁₃₂ = 2 x 2 x 3 x 11

Now the common factors of 24, 36, 60 and 132 = 2, 2 and 3

H.C.F. = 2 x 2 x 3 = 12

(v) Factor of 30 = F₃₀ = 2 x 3 x 5

Factor of 60 = F₆₀ = 2 x 2 x 3 x 5

Factor of 90 = F₉₀ = 2 x 3 x 3 x 5

and factor of 105 = F₁₀₅ = 3 x 5 x 7

Now the common factor of 30, 60, 90 and 105 = 3 and 5

H.C.F. = 3 x 5 = 15