Question

When 31513 and 34369 are divided by a certain three digit no. the remainder are equal. Find this remainder.

Answer 1

34369 - 31513 = 2856

Then we list all divisors of 2856:
1, 2, 3, 4, 6, 7, 8, 12, 14, 17, 21, 24, 28, 34, 42, 51, 56, 68, 84, 102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952, 1428, 2856

From here, we take all the 3-digit numbers:
102, 119, 136, 168, 204, 238, 357, 408, 476, 714, 952
There are 11 possible answers.

Hope this helps.