Question

If tge hcf of 65 and 117 is expressible in the form 65m-117 then find the value of m

Answer 1

HCF of 65 and 117 is 13.
65m-117=13.
65m=13+117
65m=130.
m=130÷65
=>m=2.
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Answer 2

HCF of 65 and 117

65 = 13 × 5

117 = 13 × 9

Note that 13 is the common factor between 65 and 117.

HCF of 65 and 117 is hence 13

Value of m

The HCF is expressible in the form 65 m - 117

                                          ==> 13 is expressible in the form 65 m - 117

                                          ==> 13 = 65 m - 117

                                          ==> 65 m = 117 + 13

                                          ==> 65 m = 130

                                          ==> m = 130/65

                                          ==> m = 2

The value of m is 2.

Hope it helps you ^___^

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