If `HCF` of `65` and `117` is expressible in the form `65m-117`, then the value of `m` is

Options

A. `4`
B. `2`
C. `1`
D. `3`

Answer

B

Explanation

By Euclid's divison algorithm,
`b=aq+r, l le r lt a` [dividend=`"divident" xx "quotient"` +remainder]
`Rightarrow 117=65xx1+52`
`Rightarrow 65=52xx1+13`
`Rightarrow 52=13xx4+0`
`therefore` HCF(65,117)=13`
Also, given that, HCF (65,117)=65-117
From Eqs. (i) and (ii)
65m-117=13
`Rightarrow 65m=130`
`Rightarrow m=2`