We're dividing 10233572 by 261 
Our goal is to divide 10233572 by 261.

Let's proceed to step 1:
When dividing 1 by 261, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 261

Advancing to step 2:
If we divide 10 by 261, we get 0 and a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (2) from the dividend and append it to 10, then repeat: 102 / 261

Advancing to step 3:
102 divided by 261 is 0 with a remainder of 102.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 102, we end up with 102.
Append the next digit (3) from the dividend to 102 and continue with: 1023 / 261

Step 4:
261 can be fit into 1023 3 times, resulting in a remainder of 240.
Write down 3 as next digit of the result. 
Result so far: 3.0
The remainder is 240 after subtracting 783 from 1023.
Include the next digit (3) from the dividend after 240, then repeat: 2403 / 261

Moving on to step 5:
261 can be fit into 2403 9 times, resulting in a remainder of 54.
The next digit of our result is 9. 
Result so far: 39.0
If we take 2349 away from 2403, we end up with 54.
Take the next digit (5) from the dividend and append it to 54, then repeat: 545 / 261

Advancing to step 6:
The number 261 fits into 545 2 times, leaving a remainder of 23.
Record the quotient 2 as the next digit in the result. 
Result so far: 392.0
Subtracting 522 from 545 leaves us with 23.
Take the next digit (7) from the dividend and append it to 23, then repeat: 237 / 261

Let's proceed to step 7:
When dividing 237 by 261, we get 0 with a remainder of 237.
The next digit of our result is 0. 
Result so far: 3920.0
Deduct 0 from 237 and we're left with 237.
Append the next digit (2) from the dividend to 237 and continue with: 2372 / 261

Advancing to step 8:
261 can be fit into 2372 9 times, resulting in a remainder of 23.
The next digit of our result is 9. 
Result so far: 39209.0
Subtract 2349 from 2372 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 9:
261 goes into 230 0 times with a remainder of 230.
Write down 0 as next digit of the result. 
Result so far: 39209.0
If we take 0 away from 230, we end up with 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2300, and continue the process.

Let's proceed to step 10:
The number 261 fits into 2300 8 times, leaving a remainder of 212.
Put 8 as the next digit of the answer. 
Result so far: 39209.08
The remainder is 212 after subtracting 2088 from 2300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2120, and continue the process.

Step 11:
261 can be fit into 2120 8 times, resulting in a remainder of 32.
The next digit of our result is 8. 
Result so far: 39209.088
If we take 2088 away from 2120, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

In conclusion, the division gives 39209.088 with a balance of 0.0032.