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Question

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

A
4
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B
2
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C
1
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D
3
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Solution

The correct option is B 2
Let the HCF of 65 and 117 be x.

Here, 65 = 13 × 5
117 = 13 × 3 × 3
LCM of 65 and 117 = 585

Now, product of 65 and 117 = HCF(65, 117) × LCM(65, 117)
HCF(65, 117) × 585 = 65 × 117
HCF(65, 117) = 1179
HCF(65, 117) = 13

Now, HCF(65, 117) = 13 = 65m - 117
m = 13065=2

Alternate Solution
By prime factorisation ;
117 = 3 × 3 × 13
65 = 5 × 13

Hence HCF of 117 and 65 is 13
HCF(65, 117) = 13 = 65m - 117
Hence m = 2

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