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

Answer 1

Use Euclid's algorithm to find the HCF of 65 and 117.
By Euclid's algorithm,
$$\begin{gathered} b=aq+r,0\le r<a \\ \Rightarrow 117=65\times 1+32 \\ \Rightarrow 65=52\times 1+13 \\ \Rightarrow 52=13\times 4+0 \\ \therefore \mathrm{HCF}\left(65,117\right)=13 \end{gathered}$$
It is given that HCF(65, 117) = 65m − 117.
$$\begin{gathered} \Rightarrow 65m-117=13 \\ \Rightarrow 65m=130 \\ \Rightarrow m=2 \end{gathered}$$
Hence, the correct option is option B.