Find the greatest number which divides 83, 125 and 209 leaving the same remainder in each case.
Options:  A) 19  B) 17  C) 42  D) 23  E) 32
The greatest number which divides three dividends p, q and r leaving the same remainder in each case is given by H.C.F(any two of (q - p), (r - p) and (r - q)).   For the given problem, p = 83, q = 125 and r = 209.   Hence the greatest number which divides these three leaving the same remainder in each case is H.C.F(any two of (125 - 83, 209 - 83, 209 - 125) = 42.   ANSWER:42
<result>C</result>
Find the greatest number which divides 83, 125 and 209 leaving the same remainder in each case.