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For some positive integer K, the repeating base-K representation of the (base-ten) fraction 7/51

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For some positive integer K, the repeating base-K representation of the (base-ten) fraction 7/51 is \(0.\overline{23}K\)= 0.232323.... K , then the value of K is

(a) 13 

(b) 14 

(c) 15 

(d) 16

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Correct option is (d) 16

We can expand the fraction \(0.\overline{23}K\) as follows

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