We look at the division of 666 by 21 
We're looking to find how many times 21 goes into 666.

Moving on to step 1:
When dividing 6 by 21, we get 0 with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 21

Step 2:
66 divided by 21 is 3 with a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 3.0
The remainder is 3 after subtracting 63 from 66.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 21

Step 3:
21 goes into 36 1 times with a remainder of 15.
Put 1 as the next digit of the answer. 
Result so far: 31.0
Subtracting 21 from 36 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 4:
21 goes into 150 7 times with a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 31.7
If we subtract 147 from 150, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 5:
If we divide 30 by 21, we get 1 and a remainder of 9.
The next digit of our result is 1. 
Result so far: 31.71
Subtract 21 from 30 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 6:
The number 21 fits into 90 4 times, leaving a remainder of 6.
The next digit of our result is 4. 
Result so far: 31.714
If we take 84 away from 90, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 7:
21 goes into 60 2 times with a remainder of 18.
The next digit of our result is 2. 
Result so far: 31.7142
Deduct 42 from 60 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 8:
21 can be fit into 180 8 times, resulting in a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 31.71428
If we take 168 away from 180, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
When dividing 120 by 21, we get 5 with a remainder of 15.
The next digit of our result is 5. 
Result so far: 31.714285
The remainder is 15 after subtracting 105 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 10:
150 divided by 21 is 7 with a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 31.7142857
If we subtract 147 from 150, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 11:
21 can be fit into 30 1 times, resulting in a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 31.71428571
The remainder is 9 after subtracting 21 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

In conclusion, the division gives 31.71428571 with a balance of 9e-09.