5. If the HCF of 65 and 117 is expressible in the form 65 m – 117, then the value of m is
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Answer:
By Euclid's divison algorithm, <br>
[dividend=
+remainder] <br>
<br>
<br>
<br>
HCF(65,117)=13
Rightarrow 65m=130
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25
Given ,
The HCF of 65 and 117 is expressible in the form 65m – 117
By Euclid's divison algorithm ,
117 = 65 × 1 + 52
65 = 52 × 1 + 13
52 = 13 × 4 + 0
Hence , the HCF of 65 and 117 can be expressible in the form of 65m - 117
Since , HCF of 65 and 117 can be 65m – 117
Thus ,
13 = 65m – 117
65m = 130
m = 130/65
m = 2
Hence , the value of m is 2
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