# 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