Find the common remainder.

[BMAD]

480608 , 508811 , 723217. These three numbers, when divided by a certain natural number > 1 , all yield the same remainder. What is that divisor and that remainder?

The 'best answer' will be awarded to the person who can develop an elegant method that does not utilize brute force or code.

[dark_magician_92]

the diffr b/w 1st and tnd no. Is 28203 which has 4 factors 3,7,17,79. Now 28203 must be a factor of the no. Which when acts as divisor, leads to same remainder. only 79, out of the 4 factors divides the diff of 3rd and 2nd no, so answerr should be 79

[ranga]

common factor of difference between pairs of numbers

[BMAD]

common factor of difference between pairs of numbers

Excellent idea! Now carry it out.