303977 ÷ 6 
Let's see how many times 6 fits into 303977.

Advancing to step 1:
When dividing 3 by 6, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Include the next digit (0) from the dividend after 3, then repeat: 30 / 6

On to step 2:
6 goes into 30 5 times with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 5.0
If we take 30 away from 30, we end up with 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 6

Let's proceed to step 3:
The number 6 fits into 3 0 times, leaving a remainder of 3.
The next digit of our result is 0. 
Result so far: 50.0
Subtract 0 from 3 to get 3.
Grab the next digit (9) from the dividend, add it to 3, then carry on: 39 / 6

On to step 4:
When dividing 39 by 6, we get 6 with a remainder of 3.
The next digit of our result is 6. 
Result so far: 506.0
If we subtract 36 from 39, we get 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 6

Moving on to step 5:
When dividing 37 by 6, we get 6 with a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 5066.0
Subtracting 36 from 37 leaves us with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 6

Step 6:
6 goes into 17 2 times with a remainder of 5.
The next digit of our result is 2. 
Result so far: 50662.0
Subtracting 12 from 17 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 7:
If we divide 50 by 6, we get 8 and a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 50662.8
Deduct 48 from 50 and we're left 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.

Step 8:
20 divided by 6 is 3 with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 50662.83
Subtracting 18 from 20 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.

Moving on to step 9:
6 goes into 20 3 times with a remainder of 2.
The next digit of our result is 3. 
Result so far: 50662.833
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 50662.833 with a balance of 0.0002.