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

1.	If the HCF of 65 and 117 is expressible in the form of 65m -117 then the value of m
Answer» By Euclid\'s division algorithmb = aq + r,0 ≤ r < a [∵ 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) = 65m - 117 ...(ii)From Eqs.(i) and (ii),65m - 117 = 13⇒ 65m = 130⇒ m = 2

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