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If the HCF of 65 and …

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

Posted by Gautam Choudhury 5 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 2 months ago

By Euclid's division algorithm
b = 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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