365 = 5 × 73 366 = 6 × 61 = 2 × 3 × 61 Number of non-divisors of 366 = 366 – 2^3 = 358 Number of non-divisors of 365 = 365 – 2^2 = 361 Number of shared non-divisors = 355 366 will have an extra remainder from all the shared non-divisors, so for this 366 will have an advantage of 355 over 365 Sum of 366’s remainders by the others divisors = R(366/5) + R(366/73) + R(366/365) = 1 + 1 + 1 = 3 Sum of 365’s remainders by the others divisors = R(365/2) + R(365/3) + R(365/6) + R(365/61) + R(365/122) + R(365/183) = 1 + 2 + 5 + 60 + 121 + 182 = 371 Answer = 371 – (355 + 3) = 13 , with 365’s sum of remainders being larger