582941 ÷ 6 
We want to figure out the number of times 582941 can be divided by 6.

Let's proceed to step 1:
6 goes into 5 0 times with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 6

Advancing to step 2:
The number 6 fits into 58 9 times, leaving a remainder of 4.
The next digit of our result is 9. 
Result so far: 9.0
Subtract 54 from 58 to get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 6

Moving on to step 3:
6 can be fit into 42 7 times, resulting in a remainder of 0.
The number 7 becomes the next digit in our result. 
Result so far: 97.0
If we subtract 42 from 42, we get 0.
Include the next digit (9) from the dividend after 0, then repeat: 9 / 6

Let's proceed to step 4:
6 can be fit into 9 1 times, resulting in a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 971.0
Subtracting 6 from 9 leaves us with 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 6

Let's proceed to step 5:
6 can be fit into 34 5 times, resulting in a remainder of 4.
The next digit of our result is 5. 
Result so far: 9715.0
The remainder is 4 after subtracting 30 from 34.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 6

Let's proceed to step 6:
41 divided by 6 is 6 with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 97156.0
Subtract 36 from 41 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 7:
The number 6 fits into 50 8 times, leaving a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 97156.8
Subtracting 48 from 50 leaves us with 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:
If we divide 20 by 6, we get 3 and a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 97156.83
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.

On to step 9:
20 divided by 6 is 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 97156.833
The remainder is 2 after subtracting 18 from 20.
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 97156.833 with a balance of 0.0002.