If the HCF of 65 and 117 is

Question:

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

(a) 4                         

(b) 2                          

(c) 1                         

(d) 3

Solution:

(b) By Euclid's division algorithm,

$b=a q+r, 0 \leq r

$\Rightarrow \quad 117=65 \times 1+52$

$\Rightarrow \quad 65=52 \times 1+13$

$\Rightarrow \quad 52=13 \times 4+0$

$\therefore \quad \operatorname{HCF}(65,117)=13$ $\ldots$ (i)

Also, given that, $\operatorname{HCF}(65,117)=65 m-117$ .....(ii)

From Eqs. (i) and (ii),

$65 m-117=13$

$\Rightarrow \quad 65 m=130$

$\Rightarrow \quad m=2$

Leave a comment

eSaral Gurukul

NEET

JEE Main

JEE Advanced

Our Telegram Channel

All Study Material