873641 ÷ 81 
Our goal is to divide 873641 by 81.

Step 1:
When dividing 8 by 81, we get 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Append the next digit (7) from the dividend to 8 and continue with: 87 / 81

Moving on to step 2:
The number 81 fits into 87 1 times, leaving a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 6 after subtracting 81 from 87.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 81

On to step 3:
81 goes into 63 0 times with a remainder of 63.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we subtract 0 from 63, we get 63.
Fetch the next digit (6) from the dividend, attach it to 63 and continue: 636 / 81

Let's proceed to step 4:
81 can be fit into 636 7 times, resulting in a remainder of 69.
Put 7 as the next digit of the answer. 
Result so far: 107.0
Subtract 567 from 636 to get 69.
Fetch the next digit (4) from the dividend, attach it to 69 and continue: 694 / 81

Moving on to step 5:
The number 81 fits into 694 8 times, leaving a remainder of 46.
Put 8 as the next digit of the answer. 
Result so far: 1078.0
Deduct 648 from 694 and we're left with 46.
Fetch the next digit (1) from the dividend, attach it to 46 and continue: 461 / 81

On to step 6:
461 divided by 81 is 5 with a remainder of 56.
Put 5 as the next digit of the answer. 
Result so far: 10785.0
If we take 405 away from 461, we end up with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Advancing to step 7:
81 can be fit into 560 6 times, resulting in a remainder of 74.
Write down 6 as next digit of the result. 
Result so far: 10785.6
If we subtract 486 from 560, we get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Let's proceed to step 8:
740 divided by 81 is 9 with a remainder of 11.
The number 9 becomes the next digit in our result. 
Result so far: 10785.69
The remainder is 11 after subtracting 729 from 740.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 9:
When dividing 110 by 81, we get 1 with a remainder of 29.
The next digit of our result is 1. 
Result so far: 10785.691
Subtract 81 from 110 to get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Step 10:
81 goes into 290 3 times with a remainder of 47.
Put 3 as the next digit of the answer. 
Result so far: 10785.6913
Subtracting 243 from 290 leaves us with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Going ahead to step 11:
The number 81 fits into 470 5 times, leaving a remainder of 65.
Put 5 as the next digit of the answer. 
Result so far: 10785.69135
Subtracting 405 from 470 leaves us with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Going ahead to step 12:
If we divide 650 by 81, we get 8 and a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 10785.691358
Deduct 648 from 650 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 13:
If we divide 20 by 81, we get 0 and a remainder of 20.
The next digit of our result is 0. 
Result so far: 10785.691358
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 14:
200 divided by 81 is 2 with a remainder of 38.
The number 2 becomes the next digit in our result. 
Result so far: 10785.69135802
Subtract 162 from 200 to get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The final result is 10785.69135802 with a remainder of 3.8e-08.