Question

Find the H.C.F of the following numbers using prime factorization method:

(i) 144,198
(ii) 81,117
(iii) 84,98
(iv) 225,450
(v) 170, 238
(vi) 504, 980
(vii) 150, 140, 210
(viii) 84, 120, 138
(ix) 106, 159, 265

Answer 1

(i) 144 and 198

Prime factorisation of 144 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$3 $\times$ 3
Prime factorisation of 198 = 2 $\times$ 3 $\times$ 3 $\times$ 11
∴ HCF = 2 $\times$ 3 $\times$ 3 = 18

(ii) 81 and 117

Prime factorisation of 81 = 3 $\times$3 $\times$ 3 $\times$ 3
Prime factorisation of 117 = 3 $\times$ 3 $\times$ 13
∴ HCF = 3 $\times$ 3 = 9

(iii) 84 and 98

Prime factorisation of 84 = 2 $\times$ 2 $\times$ 3 $\times$ 7
Prime factorisation of 98 = 2 $\times$ 7 $\times$ 7
∴ HCF = 2 $\times$ 7 = 14

(iv) 225 and 450

Prime factorisation of 225 = 3 $\times$ 3 $\times$ 5 $\times$ 5
Prime factorisation of 450 = 2 $\times$ 3 $\times$ 3 $\times$ 5 $\times$ 5
∴ HCF = 3 $\times$ 3 $\times$ 5 $\times$ 5 = 225

(v) 170 and 238

Prime factorisation of 170 = 2 $\times$ 5 $\times$ 17
Prime factorisation of 238 = 2 $\times$ 7 $\times$ 17
∴ HCF = 2 $\times$ 17= 34

(vi) 504 and 980
We have
Prime factorisation of 504 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 7
Prime factorisation of 980 = 2 $\times$ 2 $\times$ 5 $\times$ 7 $\times$ 7
∴ HCF = 2 $\times$ 2 $\times$ 7 = 28

(vii) 150, 140 and 210

Prime factorisation of 150 = 2 $\times$ 3 $\times$ 5 $\times$5
Prime factorisation of 140 = 2 $\times$ 2 $\times$ 5 $\times$ 7
Prime factorisation of 210 = 2 $\times$ 3 $\times$ 5 $\times$ 7
∴ HCF = 2 $\times$ 5 = 10

(viii) 84, 120 and 138

Prime factorisation of 84 = 2 $\times$ 2 $\times$ 3 $\times$ 7
Prime factorisation of 120 = 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 5
Prime factorisation of 138 = 2 $\times$ 3 $\times$ 23
∴ HCF = 2 $\times$ 3 = 6

(ix) 106, 159, and 265

Prime factorisation of 106 = 2 $\times$ 53
Prime factorisation of 159 = 3 $\times$ 53
Prime factorisation of 265 = 5 $\times$ 53
∴ HCF = 53