If $\text{HCF}(65, 117)$ is expressible in the form $65m - 117$, then the value of $m$ is:
(a) $4$
(b) $2$
(c) $1$
(d) $3$
Step-by-Step Solution
Key Concept: Find HCF(65, 117) by prime factorisation, then solve $65m - 117 = \text{HCF}$.
$65 = 5 \times 13$, $117 = 3^2 \times 13 \Rightarrow \text{HCF}(65, 117) = 13$. [0.5 Mark]
Given $65m - 117 = 13 \Rightarrow 65m = 130 \Rightarrow m = 2$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Correct HCF: 0.5 Mark
Correct value of $m$: 0.5 Mark
Correct Answer: $2$