Find the largest number that divides 245 and 1029 leaving the same remainder in each case.
Hint: such a number divides the difference of the two numbers.

Difference = 1029 - 245 = 784. The required largest number divides 784 exactly and is 784 itself (since 784 divides both leaving remainder 245-0... check: $245=784\times 0+245,1029=784\times 1+245$, same remainder 245). Largest such number = 784.