Question

If theHCF of 65 and 117 is expressible in the from 65m-117 then the value of m is .....​

Answer 1

Let us find the HCF of 65 and 117

by EUCLID'S DIVISION LEMMA

117 = 65 * 1 + 52

65 = 52 * 1 + 13

52 = 13 * 4 + 0

Last divisor is 13 when remainder became zero

HENCE, HCF of 65 and 117 is 13

now according to the question

the HCF is expressible in the form 65 m - 117

so,

13 = 65 m - 117

65 m = 13 + 117

m = 130 / 65

m = 2

Hence, the value of m is 2 .

Answer 2

Given:-

The numbers 65 and 117

To find

The value of m

A.T.Q:-

So By Euclid division lemma find the H.C.F of 65 and 117

● 117= 65×1+52

=> 65=52×1+13

=> 52 =13×4+0

So now the H.C.F of 117 and 65 is 13

And this is expressed in the form of

65m -117 =H.C.F

We have to find the Value of m

Then,

= > 65m-117=13

=> 65m=13+117

=> 65m= 130

=> m= 130/65

=> m=2[/tex]

The value of m is 2

• So let's verify

=> 65m-117=13

=> 65×2-117=3

=> 130-117= 13

=> 13=13

L.H.S =R.H.S