Question

Question 4
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

Answer 1

By Euclid's division algorithm, we can find the HCF of 65 and 117
We have $a=bq+r,0\le r<b[\because dividend=divisor\times quotient+remainder]$

If a = 117 and b -65, then
$117=65\times 1+52$

Now, take a = 65 and b = 52. We get:
$\Rightarrow 65=52\times 1+13$

Now, take a = 52 and b = 13. We get:
$\Rightarrow 52=13\times 4+0$

Since the remainder in this step is 0, the divisior, which is 13, is the HCF.
$\therefore$ HCF (65, 117) = 13
Also, given that, HCF (65, 117) = 65m - 117
65m - 117 = 13
65m = 130
m = 2

Thus, the answer is B.