We're dividing 512558 by 2 
Our goal is to divide 512558 by 2.

On to step 1:
2 goes into 5 2 times with a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Subtracting 4 from 5 leaves us with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 2

Step 2:
If we divide 11 by 2, we get 5 and a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 25.0
The remainder is 1 after subtracting 10 from 11.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 2

Let's proceed to step 3:
The number 2 fits into 12 6 times, leaving a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 256.0
The remainder is 0 after subtracting 12 from 12.
Grab the next digit (5) from the dividend, add it to 0, then carry on: 5 / 2

Advancing to step 4:
The number 2 fits into 5 2 times, leaving a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 2562.0
The remainder is 1 after subtracting 4 from 5.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 2

On to step 5:
When dividing 15 by 2, we get 7 with a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 25627.0
If we take 14 away from 15, we end up with 1.
Include the next digit (8) from the dividend after 1, then repeat: 18 / 2

Moving on to step 6:
2 goes into 18 9 times with a remainder of 0.
Write down 9 as next digit of the result. 
Result so far: 256279.0
If we subtract 18 from 18, we 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 7:
2 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 256279.0
If we subtract 0 from 0, we 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 8:
2 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 256279.0
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 quotient of the division is 256279.0, and the remainder is 0.0.