Step by step
The question
Question: work out 40 mod 8.
40 mod 8
Mod 8 means: the remainder after dividing by 8.
It is always a whole number from 0 to 7.
mod 8 = the remainder after ÷ 8
always 0 to 7
1 Divide by 8
Divide 40 by 8: 8 goes 5 times, that is 40, and 0 is left over.
40 = 8 × 5 + 0
Careful!
5 is how many times 8 goes in.
Mod asks for what is left over: 0.
Careful: not 40 mod 8 = 5 ✗
2 On the clock
Think of a clock with 8 numbers, 0 to 7.
So 40 mod 8 = 0.
40 mod 8 = 0
3 Check
Multiply back: 8 times 5, plus 0, is 40.
8 × 5 + 0 = 40 + 0 = 40
And 0 is from 0 to 7.
Right!
0 ≤ 0 < 8
Let's look back.
First: divide by 8.
Then: on the clock.
Last: check.
Answer
40 mod 8 = 0