Question

Find the H.C.F of 65 and 117 and express it in the form of 65x×117y.

Answer 1

Hey friend, Harish here.

Here is your answer:

Euclid's Division Lemma states that,

a = b ( q ) + r.

Here.

117 = 65 × 1 + 52 

65 = 52 × 1 + 13 

52 = 13 × 4 + 0

Therefore 13 is the HCF. 

Then we know that,

13 = 65 - (52 × 1) .

And ,  52 = 117 - ( 65 × 1 )

Then, 13 = 65 - (117 - 65 × 1)  

⇒ (65 × 2) - 117. = 65x - 117y

Now by comparing we get.

x = 2, y = 1.
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Hope my answer is helpful to you.