Find the hcf of 65 and 117 and express in the form of 65m+117n

 

1. Find the hcf of 65 and 117 and express in the form of 65m+117n

A) m=1 n=-1
B) m=1 n=-2
C) m=2 n=1
D) m=2 n=-1

ANSWER= (A) m=2 n=-1

Answer:

Explain:-

Let the hcf of 65 and 117 and express in the form of 65m+117n

Using Euclid Division Lemma,

117=65*1+52 ..............................(1)

65=52*1+13

52=13*4+0

HCF=13

Given HCF of 65 and 117 is express in the form of 65m+117n

therefore,

65m+117=13...........................(2)

13=65-52*1

By equation 1

13=65- (117-65*1)

13=65-117+65*1

13=65*2-117

13=65(2)+117(-1)      ..............................(3)

therefore by comparing  eq...2 and 3

m=2

n=-1

Answer completed.