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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 ______.
Options
4
2
1
3
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Solution
If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is 2.
Explanation:
Let us find the HCF of 65 and 117,
117 = 1 × 65 + 52
65 = 1 × 52 + 13
52 = 4 × 13 + 0
Hence, we get the HCF of 65 and 117 = 13.
65m – 117 = 13
65m = 117 + 13 = 130
∴ m = `130/65` = 2
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