581984 ÷ 6 
Let's see how many times 6 fits into 581984.

Step 1:
The number 6 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 6

Let's proceed to step 2:
6 goes into 58 9 times with a remainder of 4.
The next digit of our result is 9. 
Result so far: 9.0
Deduct 54 from 58 and we're left with 4.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 6

On to step 3:
6 goes into 41 6 times with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 96.0
Deduct 36 from 41 and we're left with 5.
Take the next digit (9) from the dividend and append it to 5, then repeat: 59 / 6

Advancing to step 4:
When dividing 59 by 6, we get 9 with a remainder of 5.
The number 9 becomes the next digit in our result. 
Result so far: 969.0
Subtracting 54 from 59 leaves us with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 6

Going ahead to step 5:
58 divided by 6 is 9 with a remainder of 4.
Write down 9 as next digit of the result. 
Result so far: 9699.0
If we subtract 54 from 58, we get 4.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 6

Advancing to step 6:
When dividing 44 by 6, we get 7 with a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 96997.0
Subtract 42 from 44 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
When dividing 20 by 6, we get 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 96997.3
Subtract 18 from 20 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 96997.33
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

In conclusion, the division gives 96997.33 with a balance of 0.002.