We look at the division of 583557 by 6 
We're looking to find how many times 6 goes into 583557.

Let's proceed to step 1:
5 divided by 6 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 6

Let's proceed to step 2:
If we divide 58 by 6, we get 9 and a remainder of 4.
The next digit of our result is 9. 
Result so far: 9.0
If we take 54 away from 58, we end up with 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 6

Let's proceed to step 3:
When dividing 43 by 6, we get 7 with a remainder of 1.
The next digit of our result is 7. 
Result so far: 97.0
Deduct 42 from 43 and we're left with 1.
Take the next digit (5) from the dividend and append it to 1, then repeat: 15 / 6

Going ahead to step 4:
If we divide 15 by 6, we get 2 and a remainder of 3.
The next digit of our result is 2. 
Result so far: 972.0
Deduct 12 from 15 and we're left with 3.
Include the next digit (5) from the dividend after 3, then repeat: 35 / 6

On to step 5:
When dividing 35 by 6, we get 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 9725.0
Subtract 30 from 35 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Advancing to step 6:
6 can be fit into 57 9 times, resulting in a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 97259.0
If we take 54 away from 57, we end up 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.

Let's proceed to step 7:
30 divided by 6 is 5 with a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 97259.5
If we subtract 30 from 30, 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.

Let's proceed 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.

Let's proceed to step 9:
6 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 97259.5
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 97259.5 with a remaining 0.0.