We're dividing 4261 by 23 
Our goal is to divide 4261 by 23.

On to step 1:
When dividing 4 by 23, we get 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 23

On to step 2:
The number 23 fits into 42 1 times, leaving a remainder of 19.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 19 after subtracting 23 from 42.
Include the next digit (6) from the dividend after 19, then repeat: 196 / 23

Going ahead to step 3:
If we divide 196 by 23, we get 8 and a remainder of 12.
The next digit of our result is 8. 
Result so far: 18.0
Deduct 184 from 196 and we're left with 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 23

Step 4:
121 divided by 23 is 5 with a remainder of 6.
Use 5 as the next digit of our solution. 
Result so far: 185.0
If we take 115 away from 121, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 5:
The number 23 fits into 60 2 times, leaving a remainder of 14.
Write down 2 as next digit of the result. 
Result so far: 185.2
If we take 46 away from 60, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 6:
140 divided by 23 is 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 185.26
Subtracting 138 from 140 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
23 goes into 20 0 times with a remainder of 20.
Record the quotient 0 as the next digit in the result. 
Result so far: 185.26
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 8:
The number 23 fits into 200 8 times, leaving a remainder of 16.
The next digit of our result is 8. 
Result so far: 185.2608
If we subtract 184 from 200, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 9:
160 divided by 23 is 6 with a remainder of 22.
The number 6 becomes the next digit in our result. 
Result so far: 185.26086
If we subtract 138 from 160, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 10:
When dividing 220 by 23, we get 9 with a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 185.260869
If we subtract 207 from 220, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 11:
23 goes into 130 5 times with a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 185.2608695
The remainder is 15 after subtracting 115 from 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 12:
23 goes into 150 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 185.26086956
Subtracting 138 from 150 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Our division results in 185.26086956 with a remaining 1.2e-08.