Question

14. Find the HCF of 65 and 117 and express it in the form 65x + 117y.
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Answer 1

Answer: 13

Step-by-step explanation:

65 = 5*13

117 = 9*13

Since 13 is the only and highest common factor, H.C.F. = 13.

Answer 2

Given integers are 65 and 117 such that 117>65

Applying division lemma to 65 and 117, we get

117=65×1+52

Since the remainder 52 is not equal to =0. So, apply the division lemma to the divisor 65 and the remainder 52 to get

65=52×1+13

We consider the new divisor 52 and the new remainder 13 and apply division lemma, to get

52=13×4+0

At this stage the remainder is zero. So, that last divisor or the non-zero remainder at the earlier stage i.e. 13 is the HCF of 65 and 117.

From (ii), we have

13=65−52×1

⇒13=65−(117−65×1)

⇒13=65−117+65×1

⇒13=65×2+117×(−1)

⇒13=65m+117n, where x=2 and y=−1.

Hope this will help you......

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