Question

find the hcf of65 and117 and expressed it as a linear combination of 65 and 117 ie hcf of 65 and 117= 65x+117y
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Answer 1

HCF of 65 and 117 is :

117=65×1 +52. ....(i)

65 =52×1+13. .....(ii)

52 =13×4 +0. ....(iii)

Therefore, HCF is 13.

Expressing HCF as 65x + 117y :

13 = 65-52×1. -from (ii)

13= 65 -(117-65×1)×1. -from (i)

13 =65×1 -117×1 +65×1

13= 65×2 -117×1

13 =65 ×2 +117×-1

13 = 65(2)+ 117(-1)

13 =65x +117y

Therefore, x=2 & y=-1

Hope my answer helped you