Why is 3 modulo 11 equal to 3?

Question

Why is 3 modulo 11 equal to 3? The expression in coding syntax is usually

 3 % 11

This is the remainder of dividing 3 by 11, correct? Then the result should be 11 since that would be the remainder. What am I understanding wrong?

No. If you take `3` divided by `11`, you get a quotient of `0` and a remainder of `3`. So `3 % 11` is `3`. — lurker, Feb 13 '14 at 04:04

score 2 · Answer 1 · answered Feb 13 '14 at 04:04

2

3 / 11 = 0 with 3 remaining. The answer to any n mod m can never be equal to or greater than m, by definition.

answered Feb 13 '14 at 04:04

Red Alert

score 2 · Accepted Answer · edited May 22 '14 at 14:56

2

Because

3 / 11 == 0
3 % 11 == 3
0 * 11 + 3 == 3

edited May 22 '14 at 14:56

BenMorel

answered Feb 13 '14 at 04:04

Weibo Li

score 1 · Answer 3 · answered Feb 13 '14 at 04:04

1

      0
    -------
11  | 3
    | 0
    |
    -------
      3 = Answer

answered Feb 13 '14 at 04:04

dotNET

3 Answers3