We look at the division of 508961 by 2 
We're looking to find how many times 2 goes into 508961.

Step 1:
The number 2 fits into 5 2 times, leaving a remainder of 1.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
The remainder is 1 after subtracting 4 from 5.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 2

Going ahead to step 2:
2 goes into 10 5 times with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 25.0
If we subtract 10 from 10, we get 0.
Include the next digit (8) from the dividend after 0, then repeat: 8 / 2

Let's proceed to step 3:
8 divided by 2 is 4 with a remainder of 0.
The number 4 becomes the next digit in our result. 
Result so far: 254.0
The remainder is 0 after subtracting 8 from 8.
Grab the next digit (9) from the dividend, add it to 0, then carry on: 9 / 2

Advancing to step 4:
2 can be fit into 9 4 times, resulting in a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 2544.0
Subtract 8 from 9 to get 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 2

Step 5:
16 divided by 2 is 8 with a remainder of 0.
The number 8 becomes the next digit in our result. 
Result so far: 25448.0
Subtracting 16 from 16 leaves us with 0.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 2

On to step 6:
If we divide 1 by 2, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 254480.0
If we subtract 0 from 1, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
If we divide 10 by 2, we get 5 and a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 254480.5
Subtract 10 from 10 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.

Moving on to step 8:
The number 2 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 254480.5
Subtracting 0 from 0 leaves us 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.

Advancing to step 9:
2 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 254480.5
Deduct 0 from 0 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.

The final outcome is 254480.5, with a leftover of 0.0.