How many ordered pairs of (m.n) integers satisfy m/12 = 12/n

• m/12 = 12/n
  
  => m*n = 144
  
  Now 144 = 2 * 2 * 2 * 2 * 3 * 3
  
  From the above set of prime factors of 144 , we can calculate 2 factors m & n
  
  1 x 144 = 144
  
  2 x 72 = 144
  
  3 x 48 = 144
  
  4 x 36 = 144
  
  6 x 24 = 144
  
  8 x 18 = 144
  
  9 x 16 = 144
  
  12 x 12 = 144
  
  First factor is m & second factor is n
  
  Then we interchange the values.
  
  So , 8+ 8 =16
  
  Then both negative numbers & interchange
  
  Again we get 8+8 =16
  
  16 +16 =32
  
  (12 x 12 )& (-12 x -12 ), 2 repeated pairs to be subtracted
  
  So TOTAL = 30 pairs
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