If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.

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If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is 2. Explanation: Let us find the HCF of 65 and 117, 117 = 1 $\times$ 65 + 52 65 = 1 $\times$ 52 + 13 52 = 4 $\times$ 13 + 0 Hence, we get the HCF of 65 and 117 = 13. 65m – 117 = 13 65m = 117 + 13 = 130 $\therefore$ m = $\frac{130}{65}$ = 2

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