Q) if the HCF of 65 and 117 is expressible in the form 65m-117, then the value of m is

• 1) 4
• 2) 2
• 3) 1
• 4) 3

if we find the HCF of 65 and 117, we get
\( 117 = 1 * 65 + 52\)
\(65 = 1 * 52 + 13\)
\(52 = 4 *13 + 0\)
The HCF of 65 and 117 is 13.
\(\implies\) 65m - 117 = 13
\(\implies\) 65m = 117 + 13
\(\implies\) m = \(\frac{130}{65}\)
\(\implies\) m = 2