We look at the division of 8681 by 82 
Our goal is to divide 8681 by 82.

Moving on to step 1:
If we divide 8 by 82, we get 0 and a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Fetch the next digit (6) from the dividend, attach it to 8 and continue: 86 / 82

Advancing to step 2:
86 divided by 82 is 1 with a remainder of 4.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 82 from 86 to get 4.
Grab the next digit (8) from the dividend, add it to 4, then carry on: 48 / 82

Step 3:
82 goes into 48 0 times with a remainder of 48.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Deduct 0 from 48 and we're left with 48.
Include the next digit (1) from the dividend after 48, then repeat: 481 / 82

Step 4:
82 can be fit into 481 5 times, resulting in a remainder of 71.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
The remainder is 71 after subtracting 410 from 481.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

On to step 5:
82 can be fit into 710 8 times, resulting in a remainder of 54.
Record the quotient 8 as the next digit in the result. 
Result so far: 105.8
The remainder is 54 after subtracting 656 from 710.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Let's proceed to step 6:
If we divide 540 by 82, we get 6 and a remainder of 48.
Record the quotient 6 as the next digit in the result. 
Result so far: 105.86
Subtracting 492 from 540 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 7:
When dividing 480 by 82, we get 5 with a remainder of 70.
Use 5 as the next digit of our solution. 
Result so far: 105.865
Subtracting 410 from 480 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 8:
700 divided by 82 is 8 with a remainder of 44.
The next digit of our result is 8. 
Result so far: 105.8658
If we subtract 656 from 700, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Step 9:
82 goes into 440 5 times with a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 105.86585
Subtract 410 from 440 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 10:
300 divided by 82 is 3 with a remainder of 54.
Put 3 as the next digit of the answer. 
Result so far: 105.865853
Subtracting 246 from 300 leaves us with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Going ahead to step 11:
The number 82 fits into 540 6 times, leaving a remainder of 48.
The number 6 becomes the next digit in our result. 
Result so far: 105.8658536
Subtracting 492 from 540 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Advancing to step 12:
The number 82 fits into 480 5 times, leaving a remainder of 70.
The number 5 becomes the next digit in our result. 
Result so far: 105.86585365
If we take 410 away from 480, we end up with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

In conclusion, the division gives 105.86585365 with a balance of 7e-08.