Step by step
The question
Question: work out 30 mod 7.
30 mod 7
Mod 7 means: the remainder after dividing by 7.
It is always a whole number from 0 to 6.
mod 7 = the remainder after ÷ 7
always 0 to 6
1 Divide by 7
Divide 30 by 7: 7 goes 4 times, that is 28, and 2 is left over.
30 = 7 × 4 + 2
Careful!
4 is how many times 7 goes in.
Mod asks for what is left over: 2.
Careful: not 30 mod 7 = 4 ✗
2 On the clock
Think of a clock with 7 numbers, 0 to 6.
So 30 mod 7 = 2.
30 mod 7 = 2
3 Check
Multiply back: 7 times 4, plus 2, is 30.
7 × 4 + 2 = 28 + 2 = 30
And 2 is from 0 to 6.
Right!
0 ≤ 2 < 7
Let's look back.
First: divide by 7.
Then: on the clock.
Last: check.
Answer
30 mod 7 = 2