Step by step
The question
Question: work out 17 mod 5.
17 mod 5
Mod 5 means: the remainder after dividing by 5.
It is always a whole number from 0 to 4.
mod 5 = the remainder after ÷ 5
always 0 to 4
1 Divide by 5
Divide 17 by 5: 5 goes 3 times, that is 15, and 2 is left over.
17 = 5 × 3 + 2
Careful!
3 is how many times 5 goes in.
Mod asks for what is left over: 2.
Careful: not 17 mod 5 = 3 ✗
2 On the clock
Think of a clock with 5 numbers, 0 to 4.
So 17 mod 5 = 2.
17 mod 5 = 2
3 Check
Multiply back: 5 times 3, plus 2, is 17.
5 × 3 + 2 = 15 + 2 = 17
And 2 is from 0 to 4.
Right!
0 ≤ 2 < 5
Let's look back.
First: divide by 5.
Then: on the clock.
Last: check.
Answer
17 mod 5 = 2