We're dividing 581329 by 2 
Our goal is to divide 581329 by 2.

Going ahead to step 1:
2 goes into 5 2 times with a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtracting 4 from 5 leaves us with 1.
Fetch the next digit (8) from the dividend, attach it to 1 and continue: 18 / 2

Step 2:
18 divided by 2 is 9 with a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 29.0
If we subtract 18 from 18, we get 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 2

Going ahead to step 3:
The number 2 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 290.0
If we subtract 0 from 1, we get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 2

Step 4:
13 divided by 2 is 6 with a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 2906.0
If we take 12 away from 13, we end up with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 2

Advancing to step 5:
If we divide 12 by 2, we get 6 and a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 29066.0
Subtracting 12 from 12 leaves us with 0.
Grab the next digit (9) from the dividend, add it to 0, then carry on: 9 / 2

Going ahead to step 6:
2 goes into 9 4 times with a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 290664.0
Subtracting 8 from 9 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
2 goes into 10 5 times with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 290664.5
Deduct 10 from 10 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
When dividing 0 by 2, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 290664.5
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 9:
The number 2 fits into 0 0 times, leaving a remainder of 0.
The next digit of our result is 0. 
Result so far: 290664.5
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 290664.5, with a leftover of 0.0.