We divide 588661 by 9
We want to figure out the number of times 588661 can be divided by 9.

Moving on to step 1:
5 divided by 9 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 9

Step 2:
9 can be fit into 58 6 times, resulting in a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we subtract 54 from 58, we get 4.
Grab the next digit (8) from the dividend, add it to 4, then carry on: 48 / 9

Advancing to step 3:
When dividing 48 by 9, we get 5 with a remainder of 3.
The next digit of our result is 5. 
Result so far: 65.0
Subtracting 45 from 48 leaves us with 3.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 9

Let's proceed to step 4:
9 can be fit into 36 4 times, resulting in a remainder of 0.
The next digit of our result is 4. 
Result so far: 654.0
Subtract 36 from 36 to get 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 9

Advancing to step 5:
9 goes into 6 0 times with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 6540.0
Subtracting 0 from 6 leaves us with 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 9

Going ahead to step 6:
9 goes into 61 6 times with a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 65406.0
Deduct 54 from 61 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
If we divide 70 by 9, we get 7 and a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 65406.7
The remainder is 7 after subtracting 63 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
70 divided by 9 is 7 with a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 65406.77
If we take 63 away from 70, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The final result is 65406.77 with a remainder of 0.007.