Question

when you divide a number by 14, what possible remainders could you have?

Answer 1

The numbers 0 to 13 inclusive of 13 and 1
So any number between 0 and 13 including 0 and 13
Because if you do 1/14 remainder is 1 r 13
2/14 is 1r 12
3/14 is 1 r 11
4/14 is 1 r 10
5/14 is 1 r 9
14/14 = 1 r 0

If x is a number and y is a number:
\[\frac{ x }{ y }\]
Then the number of remainders when you divide x by y is:
\[\mod(y)\]
mod means the numbers including that would be on a clock where y is at the top and their multiples for example:
\[\mod(12)\] = 0,1,2,3,4,5,6,7,8,9,10,11,and 1. Plus their multiples so 0,...2...3,4....6,6...9,.......
Or an easier way to think of it is all the numbers between 0 and (y-1) inclusive so including (y-1) and 0.

Answer 2

0,1,2,3,4,5,6,7,8,9,10,11,12,13