We divide 583557 by 6
We want to figure out the number of times 583557 can be divided by 6.

Moving on to step 1:
When dividing 5 by 6, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 6

On to step 2:
The number 6 fits into 58 9 times, leaving a remainder of 4.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
If we subtract 54 from 58, we get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

On to step 3:
If we divide 43 by 6, we get 7 and a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 97.0
If we take 42 away from 43, we end up with 1.
Take the next digit (5) from the dividend and append it to 1, then repeat: 15 / 6

On to step 4:
If we divide 15 by 6, we get 2 and a remainder of 3.
Use 2 as the next digit of our solution. 
Result so far: 972.0
Subtract 12 from 15 to get 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 6

Let's proceed to step 5:
When dividing 35 by 6, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 9725.0
If we subtract 30 from 35, we get 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 6

Going ahead to step 6:
When dividing 57 by 6, we get 9 with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 97259.0
Deduct 54 from 57 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 7:
If we divide 30 by 6, we get 5 and a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 97259.5
Subtract 30 from 30 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.

Advancing to step 8:
6 goes into 0 0 times with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 97259.5
If we subtract 0 from 0, we 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.

Moving on to step 9:
6 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 97259.5
If we subtract 0 from 0, we 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.

The final outcome is 97259.5, with a leftover of 0.0.