Let's divide 102564 by 81
Our goal is to divide 102564 by 81.

Advancing to step 1:
81 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 81

Going ahead to step 2:
81 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (2) from the dividend, attach it to 10 and continue: 102 / 81

Going ahead to step 3:
When dividing 102 by 81, we get 1 with a remainder of 21.
The next digit of our result is 1. 
Result so far: 1.0
If we take 81 away from 102, we end up with 21.
Append the next digit (5) from the dividend to 21 and continue with: 215 / 81

Step 4:
When dividing 215 by 81, we get 2 with a remainder of 53.
The next digit of our result is 2. 
Result so far: 12.0
If we take 162 away from 215, we end up with 53.
Grab the next digit (6) from the dividend, add it to 53, then carry on: 536 / 81

Let's proceed to step 5:
536 divided by 81 is 6 with a remainder of 50.
Write down 6 as next digit of the result. 
Result so far: 126.0
Deduct 486 from 536 and we're left with 50.
Fetch the next digit (4) from the dividend, attach it to 50 and continue: 504 / 81

Let's proceed to step 6:
When dividing 504 by 81, we get 6 with a remainder of 18.
Use 6 as the next digit of our solution. 
Result so far: 1266.0
Subtracting 486 from 504 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 7:
The number 81 fits into 180 2 times, leaving a remainder of 18.
The next digit of our result is 2. 
Result so far: 1266.2
If we take 162 away from 180, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 8:
180 divided by 81 is 2 with a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 1266.22
The remainder is 18 after subtracting 162 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

After the division, we end up with 1266.22 and a remainder of 0.018.