429561 ÷ 81 
Our goal is to divide 429561 by 81.

Step 1:
81 goes into 4 0 times with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 81

Let's proceed to step 2:
42 divided by 81 is 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Bring next digit (9) of the dividend behind the 42 and repeat the process: 429 / 81

Let's proceed to step 3:
81 can be fit into 429 5 times, resulting in a remainder of 24.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
The remainder is 24 after subtracting 405 from 429.
Include the next digit (5) from the dividend after 24, then repeat: 245 / 81

Advancing to step 4:
245 divided by 81 is 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 53.0
The remainder is 2 after subtracting 243 from 245.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 81

Going ahead to step 5:
26 divided by 81 is 0 with a remainder of 26.
Record the quotient 0 as the next digit in the result. 
Result so far: 530.0
Subtracting 0 from 26 leaves us with 26.
Include the next digit (1) from the dividend after 26, then repeat: 261 / 81

Step 6:
The number 81 fits into 261 3 times, leaving a remainder of 18.
Use 3 as the next digit of our solution. 
Result so far: 5303.0
Subtract 243 from 261 to get 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:
If we divide 180 by 81, we get 2 and a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 5303.2
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.

Going ahead to step 8:
The number 81 fits into 180 2 times, leaving a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 5303.22
Deduct 162 from 180 and we're left 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.

In conclusion, the division gives 5303.22 with a balance of 0.018.