We're dividing 583608 by 10 
Let's see how many times 10 fits into 583608.

Advancing to step 1:
10 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (8) from the dividend, add it to 5, then carry on: 58 / 10

On to step 2:
10 goes into 58 5 times with a remainder of 8.
The next digit of our result is 5. 
Result so far: 5.0
If we subtract 50 from 58, we get 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 10

Moving on to step 3:
If we divide 83 by 10, we get 8 and a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 58.0
Subtracting 80 from 83 leaves us with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 10

Step 4:
If we divide 36 by 10, we get 3 and a remainder of 6.
The number 3 becomes the next digit in our result. 
Result so far: 583.0
Subtracting 30 from 36 leaves us with 6.
Fetch the next digit (0) from the dividend, attach it to 6 and continue: 60 / 10

Advancing to step 5:
When dividing 60 by 10, we get 6 with a remainder of 0.
Use 6 as the next digit of our solution. 
Result so far: 5836.0
Subtract 60 from 60 to get 0.
Include the next digit (8) from the dividend after 0, then repeat: 8 / 10

Let's proceed to step 6:
8 divided by 10 is 0 with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 58360.0
If we take 0 away from 8, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 7:
When dividing 80 by 10, we get 8 with a remainder of 0.
Write down 8 as next digit of the result. 
Result so far: 58360.8
Subtracting 80 from 80 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.

Step 8:
10 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 58360.8
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.

Let's proceed to step 9:
10 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 58360.8
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 58360.8, with a leftover of 0.0.