Question  Find remainder if following  expression  is divided by  7   
                         19  X 20  X  22 X  23 X 24

         Conventional method is multiplying all numbers then divided by 7  . It takes lot of time  , you can do this  
         question mentally .How?  First we divide  individually all numbers by 7 and take all remainders   as a first 
         step . Now multiply  all remainders  and again divide by 7 and take required   remainder . That  is    our
          answer 

           19  X 20  X  22 X  23 X 24
          
           5 X  6 X   1 X     2     X   3 =  180  (  Multiplications of remainders)   

           180/7  =   25 +  remainder 5

          We make it more easy
          Take two remainders multiplication  and divide it  by 7    ,again take others  three remainders multiplication  and 
          divide it  by 7 

          (5 X  6) X  ( 1 X     2     X   3) =      2  X 6   (  Multiplications of remainders) 
          
          =    12/ 7  =  1+ remainder 5
         

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