We look at the division of 575839 by 66 
Our goal is to divide 575839 by 66.

Advancing to step 1:
If we divide 5 by 66, we get 0 and a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (7) from the dividend after 5, then repeat: 57 / 66

Step 2:
57 divided by 66 is 0 with a remainder of 57.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 57 and we're left with 57.
Fetch the next digit (5) from the dividend, attach it to 57 and continue: 575 / 66

Moving on to step 3:
The number 66 fits into 575 8 times, leaving a remainder of 47.
Put 8 as the next digit of the answer. 
Result so far: 8.0
Subtract 528 from 575 to get 47.
Append the next digit (8) from the dividend to 47 and continue with: 478 / 66

Step 4:
If we divide 478 by 66, we get 7 and a remainder of 16.
The number 7 becomes the next digit in our result. 
Result so far: 87.0
If we take 462 away from 478, we end up with 16.
Include the next digit (3) from the dividend after 16, then repeat: 163 / 66

Moving on to step 5:
66 goes into 163 2 times with a remainder of 31.
Record the quotient 2 as the next digit in the result. 
Result so far: 872.0
Subtracting 132 from 163 leaves us with 31.
Append the next digit (9) from the dividend to 31 and continue with: 319 / 66

Advancing to step 6:
319 divided by 66 is 4 with a remainder of 55.
The next digit of our result is 4. 
Result so far: 8724.0
Deduct 264 from 319 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

On to step 7:
The number 66 fits into 550 8 times, leaving a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 8724.8
The remainder is 22 after subtracting 528 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 8:
When dividing 220 by 66, we get 3 with a remainder of 22.
Write down 3 as next digit of the result. 
Result so far: 8724.83
The remainder is 22 after subtracting 198 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 9:
220 divided by 66 is 3 with a remainder of 22.
The number 3 becomes the next digit in our result. 
Result so far: 8724.833
If we subtract 198 from 220, 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.

The final outcome is 8724.833, with a leftover of 0.0022.