558584 ÷ 10 
We're looking to find how many times 10 goes into 558584.

Advancing to step 1:
5 divided by 10 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 10

Moving on to step 2:
When dividing 55 by 10, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 50 from 55 leaves us with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 10

Step 3:
When dividing 58 by 10, we get 5 with a remainder of 8.
Write down 5 as next digit of the result. 
Result so far: 55.0
If we subtract 50 from 58, we get 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 10

Going ahead to step 4:
If we divide 85 by 10, we get 8 and a remainder of 5.
Write down 8 as next digit of the result. 
Result so far: 558.0
The remainder is 5 after subtracting 80 from 85.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 10

Moving on to step 5:
The number 10 fits into 58 5 times, leaving a remainder of 8.
Record the quotient 5 as the next digit in the result. 
Result so far: 5585.0
If we subtract 50 from 58, we get 8.
Fetch the next digit (4) from the dividend, attach it to 8 and continue: 84 / 10

On to step 6:
The number 10 fits into 84 8 times, leaving a remainder of 4.
The next digit of our result is 8. 
Result so far: 55858.0
Deduct 80 from 84 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 7:
10 can be fit into 40 4 times, resulting in a remainder of 0.
Write down 4 as next digit of the result. 
Result so far: 55858.4
If we subtract 40 from 40, 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.

Advancing to step 8:
10 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 55858.4
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.

Let's proceed to step 9:
If we divide 0 by 10, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 55858.4
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.

After the division, we end up with 55858.4 and a remainder of 0.0.