Step by step
The question
Question: work out 100 mod 7.
100 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 100 by 7: 7 goes 14 times, that is 98, and 2 is left over.
100 = 7 × 14 + 2
Careful!
14 is how many times 7 goes in.
Mod asks for what is left over: 2.
Careful: not 100 mod 7 = 14 ✗
So 100 mod 7 = 2.
100 mod 7 = 2
2 Check
Multiply back: 7 times 14, plus 2, is 100.
7 × 14 + 2 = 98 + 2 = 100
And 2 is from 0 to 6.
Right!
0 ≤ 2 < 7
Let's look back.
First: divide by 7.
Last: check.
Answer
100 mod 7 = 2