We look at the division of 769633 by 81 
We're looking to find how many times 81 goes into 769633.

On to step 1:
81 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 81

Advancing to step 2:
76 divided by 81 is 0 with a remainder of 76.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 76 after subtracting 0 from 76.
Append the next digit (9) from the dividend to 76 and continue with: 769 / 81

Advancing to step 3:
When dividing 769 by 81, we get 9 with a remainder of 40.
The next digit of our result is 9. 
Result so far: 9.0
The remainder is 40 after subtracting 729 from 769.
Grab the next digit (6) from the dividend, add it to 40, then carry on: 406 / 81

Step 4:
If we divide 406 by 81, we get 5 and a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 95.0
Subtracting 405 from 406 leaves us with 1.
Include the next digit (3) from the dividend after 1, then repeat: 13 / 81

Let's proceed to step 5:
The number 81 fits into 13 0 times, leaving a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 950.0
If we take 0 away from 13, we end up with 13.
Grab the next digit (3) from the dividend, add it to 13, then carry on: 133 / 81

Moving on to step 6:
133 divided by 81 is 1 with a remainder of 52.
The number 1 becomes the next digit in our result. 
Result so far: 9501.0
If we take 81 away from 133, we end up with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 7:
When dividing 520 by 81, we get 6 with a remainder of 34.
Record the quotient 6 as the next digit in the result. 
Result so far: 9501.6
Deduct 486 from 520 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 8:
The number 81 fits into 340 4 times, leaving a remainder of 16.
Write down 4 as next digit of the result. 
Result so far: 9501.64
The remainder is 16 after subtracting 324 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 9:
If we divide 160 by 81, we get 1 and a remainder of 79.
Record the quotient 1 as the next digit in the result. 
Result so far: 9501.641
Subtract 81 from 160 to get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

On to step 10:
81 can be fit into 790 9 times, resulting in a remainder of 61.
Record the quotient 9 as the next digit in the result. 
Result so far: 9501.6419
Deduct 729 from 790 and we're left with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Let's proceed to step 11:
81 goes into 610 7 times with a remainder of 43.
The next digit of our result is 7. 
Result so far: 9501.64197
Deduct 567 from 610 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Going ahead to step 12:
81 can be fit into 430 5 times, resulting in a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 9501.641975
The remainder is 25 after subtracting 405 from 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 13:
The number 81 fits into 250 3 times, leaving a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 9501.6419753
If we take 243 away from 250, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 14:
81 goes into 70 0 times with a remainder of 70.
Use 0 as the next digit of our solution. 
Result so far: 9501.6419753
Subtracting 0 from 70 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.

In conclusion, the division gives 9501.6419753 with a balance of 7e-08.