We look at the division of 597588 by 9 
We're looking to find how many times 9 goes into 597588.

Let's proceed to step 1:
9 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (9) from the dividend to 5 and continue with: 59 / 9

On to step 2:
9 goes into 59 6 times with a remainder of 5.
Put 6 as the next digit of the answer. 
Result so far: 6.0
The remainder is 5 after subtracting 54 from 59.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 9

On to step 3:
When dividing 57 by 9, we get 6 with a remainder of 3.
Write down 6 as next digit of the result. 
Result so far: 66.0
If we take 54 away from 57, we end up with 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 9

On to step 4:
35 divided by 9 is 3 with a remainder of 8.
Write down 3 as next digit of the result. 
Result so far: 663.0
If we subtract 27 from 35, we get 8.
Bring next digit (8) of the dividend behind the 8 and repeat the process: 88 / 9

Let's proceed to step 5:
If we divide 88 by 9, we get 9 and a remainder of 7.
Use 9 as the next digit of our solution. 
Result so far: 6639.0
Subtracting 81 from 88 leaves us with 7.
Include the next digit (8) from the dividend after 7, then repeat: 78 / 9

Advancing to step 6:
9 can be fit into 78 8 times, resulting in a remainder of 6.
The next digit of our result is 8. 
Result so far: 66398.0
Subtracting 72 from 78 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 7:
60 divided by 9 is 6 with a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 66398.6
If we take 54 away from 60, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 8:
9 can be fit into 60 6 times, resulting in a remainder of 6.
Use 6 as the next digit of our solution. 
Result so far: 66398.66
Subtract 54 from 60 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The final result is 66398.66 with a remainder of 0.006.