The following question is taken from ‘Amusements in Mathematics’ by Henry Ernest Dudeney. This book was first published in 1917. Can you solve it without the use of a computer?
127. SIMPLE DIVISION
Sometimes a very simple question in elementary arithmetic will cause a good deal of perplexity. For example, I want to divide the four numbers, 701, 1,059, 1,417, and 2,312, by the largest number possible that will leave the same remainder in every case. How am I to set to work? Of course, by laborious system of trial one can in time discover the answer, but there is quite a simple method of doing it if you can only find it.