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.
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