Question

Find the HCF of 65 and 117 and express it in the form of 65m+117n?​

Answer 1

Answer:

hello mate..

Step-by-step explanation:

ER

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



=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 m=2 and n=−1.

hope you get your answer

plz follow me follow back will be done

plz mark as brain list answer ❤✅❤

Answer 2

Answer:

heyyy,

Euclid's Division Lemma :-

a = bq +r

117 > 65

117 = 65 × 1 + 52 ----> [ 2 ]

65 = 52 x 1 + 13 -----> [1]

52 = 13 x 4 + 0

HCF = 13

13 = 65m + 117n

From [ 1] ,

13 = 65 - 52 x 1

From [2] ,

52 = 117 - 65 x 1 ----> [3]

Hence ,

13 = 65 - [ 117 - 65 x 1 ] ------> from [3]

= 65 x 2 - 117

= 65 x 2 + 117 x [-1 ]

m = 2

n = -1

Step-by-step explanation:

PLZ MARK ME AS A BRAINLIEST

FOLLOW ME

I HOPE THIS IS HELPFUL FOR YOU AND OTHERS