We look at the division of 769564 by 81 
We want to figure out the number of times 769564 can be divided by 81.

Step 1:
If we divide 7 by 81, we get 0 and 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.
Fetch the next digit (6) from the dividend, attach it to 7 and continue: 76 / 81

Step 2:
76 divided by 81 is 0 with a remainder of 76.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 76, we get 76.
Grab the next digit (9) from the dividend, add it to 76, then carry on: 769 / 81

Advancing to step 3:
When dividing 769 by 81, we get 9 with a remainder of 40.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
If we take 729 away from 769, we end up with 40.
Fetch the next digit (5) from the dividend, attach it to 40 and continue: 405 / 81

Going ahead to step 4:
The number 81 fits into 405 5 times, leaving a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 95.0
If we take 405 away from 405, we end up with 0.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 81

Step 5:
When dividing 6 by 81, we get 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 950.0
Subtracting 0 from 6 leaves us with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 81

Step 6:
64 divided by 81 is 0 with a remainder of 64.
Use 0 as the next digit of our solution. 
Result so far: 9500.0
Deduct 0 from 64 and we're left with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Moving on to step 7:
When dividing 640 by 81, we get 7 with a remainder of 73.
Record the quotient 7 as the next digit in the result. 
Result so far: 9500.7
Deduct 567 from 640 and we're left with 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Step 8:
81 goes into 730 9 times with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 9500.79
Deduct 729 from 730 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 9:
The number 81 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 9500.79
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 10:
100 divided by 81 is 1 with a remainder of 19.
Record the quotient 1 as the next digit in the result. 
Result so far: 9500.7901
Deduct 81 from 100 and we're left with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 11:
81 goes into 190 2 times with a remainder of 28.
Write down 2 as next digit of the result. 
Result so far: 9500.79012
Subtracting 162 from 190 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 12:
When dividing 280 by 81, we get 3 with a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 9500.790123
If we subtract 243 from 280, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Advancing to step 13:
If we divide 370 by 81, we get 4 and a remainder of 46.
Record the quotient 4 as the next digit in the result. 
Result so far: 9500.7901234
If we subtract 324 from 370, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Step 14:
If we divide 460 by 81, we get 5 and a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 9500.79012345
Subtract 405 from 460 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Our division results in 9500.79012345 with a remaining 5.5e-08.