81086821 ÷ 829 
Our goal is to divide 81086821 by 829.

Advancing to step 1:
8 divided by 829 is 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Bring next digit (1) of the dividend behind the 8 and repeat the process: 81 / 829

Advancing to step 2:
When dividing 81 by 829, we get 0 with a remainder of 81.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 81 after subtracting 0 from 81.
Include the next digit (0) from the dividend after 81, then repeat: 810 / 829

Step 3:
810 divided by 829 is 0 with a remainder of 810.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 810 and we're left with 810.
Take the next digit (8) from the dividend and append it to 810, then repeat: 8108 / 829

On to step 4:
829 goes into 8108 9 times with a remainder of 647.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
If we subtract 7461 from 8108, we get 647.
Fetch the next digit (6) from the dividend, attach it to 647 and continue: 6476 / 829

Going ahead to step 5:
829 goes into 6476 7 times with a remainder of 673.
Put 7 as the next digit of the answer. 
Result so far: 97.0
Subtract 5803 from 6476 to get 673.
Append the next digit (8) from the dividend to 673 and continue with: 6738 / 829

Step 6:
If we divide 6738 by 829, we get 8 and a remainder of 106.
The next digit of our result is 8. 
Result so far: 978.0
If we subtract 6632 from 6738, we get 106.
Grab the next digit (2) from the dividend, add it to 106, then carry on: 1062 / 829

Moving on to step 7:
1062 divided by 829 is 1 with a remainder of 233.
The number 1 becomes the next digit in our result. 
Result so far: 9781.0
Subtract 829 from 1062 to get 233.
Fetch the next digit (1) from the dividend, attach it to 233 and continue: 2331 / 829

Let's proceed to step 8:
If we divide 2331 by 829, we get 2 and a remainder of 673.
Use 2 as the next digit of our solution. 
Result so far: 97812.0
If we take 1658 away from 2331, we end up with 673.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6730, and continue the process.

Advancing to step 9:
829 can be fit into 6730 8 times, resulting in a remainder of 98.
Write down 8 as next digit of the result. 
Result so far: 97812.8
Subtract 6632 from 6730 to get 98.
Since there are no more digits in the dividend, we add a zero to the remainder making it 980, and continue the process.

Going ahead to step 10:
829 goes into 980 1 times with a remainder of 151.
The number 1 becomes the next digit in our result. 
Result so far: 97812.81
Subtracting 829 from 980 leaves us with 151.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1510, and continue the process.

Let's proceed to step 11:
The number 829 fits into 1510 1 times, leaving a remainder of 681.
Put 1 as the next digit of the answer. 
Result so far: 97812.811
Subtracting 829 from 1510 leaves us with 681.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6810, and continue the process.

The final result is 97812.811 with a remainder of 0.0681.