Step by step
The question
Question: work out 23 mod 4.
23 mod 4
Mod 4 means: the remainder after dividing by 4.
It is always a whole number from 0 to 3.
mod 4 = the remainder after ÷ 4
always 0 to 3
1 Divide by 4
Divide 23 by 4: 4 goes 5 times, that is 20, and 3 is left over.
23 = 4 × 5 + 3
Careful!
5 is how many times 4 goes in.
Mod asks for what is left over: 3.
Careful: not 23 mod 4 = 5 ✗
2 On the clock
Think of a clock with 4 numbers, 0 to 3.
So 23 mod 4 = 3.
23 mod 4 = 3
3 Check
Multiply back: 4 times 5, plus 3, is 23.
4 × 5 + 3 = 20 + 3 = 23
And 3 is from 0 to 3.
Right!
0 ≤ 3 < 4
Let's look back.
First: divide by 4.
Then: on the clock.
Last: check.
Answer
23 mod 4 = 3