Find the greatest number by which 78, 153 and 228 will be divided so that it leaves the same remainder in every case?
(A) 25
(B) 75
(C) 77
(D) 76

• by verification it is 75
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• by checking all it wll be : 75
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• 75 it is a question of hcf
  let the no be k
  so requred no is 78-k;153-k;228-k;
  we know that difference of no is also give the hcf
  so
  153-k-(78-k)=75
  228-k-(153-k)=75
  228-k-(153-k)=150
  using these three no we find hcfas 75
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• go for hit & trial from options as here if you find hcf it will be 3
  now the greatest number in option is 75 you can easily see that by dividing 78/75=3 & 153/75=3 now do 225/75=3 so it is 75
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• answer is 75
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