If the HCF of 65 and 117 is expressible in the form 65m -117, then the value of m is


According to Euclid’s division algorithm,


b = a × q + r, 0 ≤ r < a [using, dividend = divisor × quotient + remainder]


117 = 65 × 1 + 52


65 = 52 × 1 + 13


52 = 13 × 4 + 0


HCF (65, 117) = 13 (i)


Also given that, HCF (65, 117) = 65 m – 117


65 m – 117 = 13 [from (i)]


65 m = 130


m = 2

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