Question

9. If the H.C.F. of 65 and117 is of the form 65k - 117 then K?​

Answer 1

Answer:

By Euclid's division algorithm

117=65×1+52 →(1)

65=52×1+13 →(2)

52=13×4+0 →(3)

Therefore 13 is HCF f (65,117)

Now going backward,

13=65+52×(−1)

13=65+[117−65×1]×(−1)

[From (1)]

13=65×2+117×(−1)

∴m=2n=−1

Answer 2

Answer:

Step-by-step explanation:

First, let’s find the HCF of 65 and 117

a=117 and b=65

According to Euclid’s division Lemma:-

a=bq+r

117 = 65 ( 1 ) + ( 52 )

Now, a=65 and b=52

65 = 52 ( 1 ) + ( 13 )

Now, a=52 and b=13

52 = 13 ( 4 ) + ( 0 )

Hence the H.C.F of 65 and 117 is 13

Given;

65k - 117 = 13

65k = 13 + 117

65k = 130

k = 130 / 65

k = 2

Hence, the value of ‘k’ is ‘2’.