We look at the division of 578601 by 6 
We're looking to find how many times 6 goes into 578601.

Advancing to step 1:
6 goes into 5 0 times with 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.
Fetch the next digit (7) from the dividend, attach it to 5 and continue: 57 / 6

Moving on to step 2:
6 can be fit into 57 9 times, resulting in a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
Deduct 54 from 57 and we're left with 3.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 6

On to step 3:
If we divide 38 by 6, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 96.0
If we take 36 away from 38, we end up with 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 6

Going ahead to step 4:
6 can be fit into 26 4 times, resulting in a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 964.0
Deduct 24 from 26 and we're left with 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 6

Moving on to step 5:
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: 9643.0
Subtracting 18 from 20 leaves us with 2.
Grab the next digit (1) from the dividend, add it to 2, then carry on: 21 / 6

Step 6:
The number 6 fits into 21 3 times, leaving a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 96433.0
The remainder is 3 after subtracting 18 from 21.
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:
When dividing 30 by 6, we get 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 96433.5
Deduct 30 from 30 and we're left 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.

Going ahead to step 8:
If we divide 0 by 6, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 96433.5
Deduct 0 from 0 and we're left 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.

Going ahead to step 9:
If we divide 0 by 6, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 96433.5
If we take 0 away from 0, we end up 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.

In conclusion, the division gives 96433.5 with a balance of 0.0.