Biggest Divisor Same Remainder

What is the largest number that, when divided into each of 1905, 2587, 3951, 7020 and 8725, leaves the same remainder each time?

When a problem seems difficult a good strategy is to try a simple case.

The diagram should help you to find the answer to the same question for 79, 35 and 57 and it should give you a hint for the method to use for the more difficult problem.

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This activity is adapted from the NRICH task Expenses with permission of the University of Cambridge. All rights reserved. Explore NRICH for many other rich mathematical activities.