Finding the largest no which divides 2 or more nos which leaves the same/different remainder

Find the largest number which divides 55,127 and 175 so as to leave the same remainder in each case .

Find the largest number which divides 62,132 and 237 to leave the same remainder in each case.

Find the least number which when divided by 35,56 and 91 leaves the same remainder 7 in each case.

Find the largest number which divides 1305, 4665 and 6905 leaving same remainder in each case.Also, find the common remainder.

Find the largest number which will divide 1305 , 4665 and 6905 and leaves equal remainder in each case.