Question

use euclid's division algorithm to find the hcf of 136,170&255

Answer 1

136 = 2^3 × 17
170 = 2 × 5 ×17
255 = 3 × 5 × 17

HCF( 136,170,255) = 17

Answer 2

Euclid division lemma:-
a = bq + r
0 ≤ r < b

First,find the HCF of 255 and 170

» 255 = 170(1) + 85
170 = 85(2) + 0

HCF of 255 and 170 is 85

Now find the HCF of 136 and 85

» 136 = 85(1) + 51
85 = 51(1) + 34
51 = 34(1) + 17
34 = 17(2) + 0

HCF of 136 and 85 is 17

Therefore! HCF (136,170,255) = 17