Question

Fimd the HCF of 65 and 117 and express it in the form of 65m +117n

Answer 1

Solution:-

On dividing 117 by 65, we get

117=65×1+52 .....(1)

65=52×1+13 .......(2)

52=13×4+0 .....(3)

Therefore, hcf (65,117) = 13.

Now,from (2),we get

65=52×1+13

=> 13=65-52×1

=> 13 = 65- (117-65×1). [ From (1)]

=> 13 = 65-117×1-65×1

=> 13=65×2+117×(-1)

Therefore, m= 2 and n = -1.

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