Question

find the hcf of 65 and 117 and express it in the form 65x and 117y

Answer 1

HCF of 117 and 65,

117= 65*1 +52
62= 52*1+13
here remainder becomes 0.
Therefore HCF of 65 and 117 is 13
HCF 13 can be expressed in the following form,
659(2)+117(-1)= 13
==> 130-117= 13
So value of x is 2 and value of y is -1
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Answer 2

Solutions 

Number                      GCF Divisor                Factors of Number

117                             117 ÷ 13 = 9                 1, 3, 9, 13, 39, 117

65                                65 ÷ 13 = 5                   1, 5, 13, 65 

According to my calculations, the greatest common factor of the numbers 117 and 65 is 13. 

GCF 13 can be expressed in the following form,

659(2)+117(-1)= 13

==> 130-117= 13

So the value of the variable x is 2 and value of variable y is -1