Question
Thu May 05, 2011 By: Utkarsh Sahu

Find the greatest number that will divide 55,127 and 175 so as to leave same remainder in each case.

Expert Reply
Thu May 05, 2011
take first two highest numbers of  (55,127and 175)
By Euclid divison lemma,
      175 = 127*1 + 48        (where 175 is divident,127 is divisor,1is quotient and 48 is remainder)
now,
      127 = 48*2 + 31
      48   = 31*1 + 17
      31   = 17*1 + 14
      17   = 14*1 + 3
      14   = 3*4   + 2
       3   =  2*1  +  1
       2   =  1*2 + 0
Then 1 is hcf of these two number 
Take 1 and last no. of (55,127and 175)
 
By Euclid divison lemma,
      55 = 1*55 + 0
So, 1 is the hcf of (55,127and 175) and leave same remainder in each case 0
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