Question

find the HCF of 65 and 117 and express it in the form of 65x+117y​

Answer 1

Step-by-step explanation:

Applying division lemma to 65 and 117, we get 117 = 65 × 1 + 52

Since the remainder 52 = 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

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 = 65 m + 117n, where m=2 and n=−1.