Step by step
The question
Question: work out −20 mod 6.
−20 mod 6
Mod 6 means: the remainder after dividing by 6.
It is always a whole number from 0 to 5.
mod 6 = the remainder after ÷ 6
always 0 to 5
1 Divide by 6
Divide −20 by 6.
For a negative number we go down to the multiple of 6 just below it: 6 × (−4) = −24.
Then up 4.
−20 = 6 × (−4) + 4
Careful!
A remainder is never negative.
We go down to the multiple just below, then count up.
Careful: not −20 mod 6 = −2 ✗
2 On the clock
Think of a clock with 6 numbers, 0 to 5.
So −20 mod 6 = 4.
−20 mod 6 = 4
3 Check
Multiply back: 6 times (−4), plus 4, is −20.
6 × (−4) + 4 = −24 + 4 = −20
And 4 is from 0 to 5.
Right!
0 ≤ 4 < 6
Let's look back.
First: divide by 6.
Then: on the clock.
Last: check.
Answer
−20 mod 6 = 4