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State whether the following statement is true or false.

If the HCF of 65 and 117 can be expressed in form $65 m - 117$ , then the value of $m$ is 4.

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True

False

answer is B.

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Detailed Solution

It is given that the HCF of 65 and 117 can be expressed in form

65 m - 117

.
The prime factor of 65 and 117 are,

65 = 5 \times 13

117 = 3 \times 3 \times 13

Then, the H.C.F. of 65 and 117 is 13.
Then,

⇒ 65 m − 117 = 13 ⇒ 65 m = 13 + 117 ⇒ 65 m = 130

⇒ m = 13065 ∴ m = 2

So, if the HCF of 65 and 117 can be expressed in form

65 m - 117

, then the value of

m

is 2.
Therefore, given statement is false.
Hence, option 2 is correct.

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