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Question

Question 4
If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is

A) 4
B) 2
C) 1
D) 3

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Solution

The answer is B.
By Euclid's division algorithm,
b = aq+r,0r<a [ dividend = divisor×quotient + remainder]
117=65×1+52
65=52×1+13
52=13×4+0
HCF (65, 117) = 13
Also, given that, HCF (65, 117) = 65m - 117
65m - 117 = 13
65m = 130
m = 2

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