In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been

 5 | x                z = 13 x 1 + 12  = 25
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 9 | y - 4            y = 9 x z + 8  = 9 x 25 + 8  = 233
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 13| z - 8            x = 5 x y + 4  = 5 x 233 + 4  = 1169
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   | 1 -12
  
  585) 1169 (1
       585
       ---
       584
       ---
       
  Therefore, on dividing the number by 585, remainder = 584.