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Question

If the HCF of 65 and 117 is expressible in the form 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


Step 1: Explanation for correct option.

For option (B): 2

As, 65=5×13

And 117=9×13

So, HCF of 65 and 117is 13

Now according to the given condition,

65m-117=13

65m=117+13

65m=130

m=2

So option (B) is correct

Step 2: Explanation for incorrect option.

For option (A): 4

If m=4, then HCF =654-117

=260-117

=143, which is not equals to 13

So option (A) is incorrect

For option (C): 1

If m=1, then HCF =651-117

=-52, which is not equals to 13

So option (C) is incorrect

For option (D): 3

If m=3, then HCF =653-117

=195-117

=78, which is not equals to 13

So option (D) is incorrect

Hence, the correct option is (B).


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