Largest Possible Remainder

October 16, 2015

The result of dividing a number n by a divisor d is a quotient q and a remainder r. Given a fixed n and a divisor d in the range 1 ≤ d < n, find the divisor that produces the largest possible remainder. For instance, given n = 20 and 1 ≤ d < 10, the largest remainder is 6 when the divisor d is 7.

Your task is to write a program that finds the largest possible remainder. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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