(B) To find the $HCF$ of $65$ and $117$ using Euclid's division algorithm:$117 = 65 \times 1 + 52$$65 = 52 \times 1 + 13$$52 = 13 \times 4 + 0$Therefo

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(B) To find the $HCF$ of $65$ and $117$ using Euclid's division algorithm:$117 = 65 \times 1 + 52$$65 = 52 \times 1 + 13$$52 = 13 \times 4 + 0$Therefore,the $HCF(65, 117) = 13$.Given that the $HCF$ is expressible as $65m - 117$,we set up the equation:$65m - 117 = 13$$65m = 13 + 117$$65m = 130$$m = \frac{130}{65}$$m = 2$