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pls answer this arithmetic problem?

pls explain the steps with example:

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

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Brute force reveals that the set of positive integer solutions is {1,5,7,35} of which 35 is the largest.

Not sure about how to solve more intelligently.

@Geezah: I interpreted "62,132,237" to mean "62, 132, and 237".

@gianlino: Thanks! It's so simple now that you point it out.