We're dividing 581616 by 9 
We want to figure out the number of times 581616 can be divided by 9.

Step 1:
The number 9 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 9

On to step 2:
9 can be fit into 58 6 times, resulting in a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Subtracting 54 from 58 leaves us with 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 9

Advancing to step 3:
The number 9 fits into 41 4 times, leaving a remainder of 5.
Use 4 as the next digit of our solution. 
Result so far: 64.0
Deduct 36 from 41 and we're left with 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 9

Moving on to step 4:
9 can be fit into 56 6 times, resulting in a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 646.0
If we take 54 away from 56, we end up with 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 9

On to step 5:
9 can be fit into 21 2 times, resulting in a remainder of 3.
Record the quotient 2 as the next digit in the result. 
Result so far: 6462.0
If we subtract 18 from 21, we get 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 9

Let's proceed to step 6:
36 divided by 9 is 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 64624.0
Subtract 36 from 36 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.

On to step 7:
The number 9 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 64624.0
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.

Let's proceed to step 8:
9 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 64624.0
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.

The final outcome is 64624.0, with a leftover of 0.0.