Let's divide 778424 by 6
Our goal is to divide 778424 by 6.

Advancing to step 1:
6 can be fit into 7 1 times, resulting in a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 6 from 7 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Let's proceed to step 2:
6 can be fit into 17 2 times, resulting in a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 12.0
If we subtract 12 from 17, we get 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 6

Moving on to step 3:
6 can be fit into 58 9 times, resulting in a remainder of 4.
Use 9 as the next digit of our solution. 
Result so far: 129.0
Subtracting 54 from 58 leaves us with 4.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 6

On to step 4:
The number 6 fits into 44 7 times, leaving a remainder of 2.
The next digit of our result is 7. 
Result so far: 1297.0
Subtract 42 from 44 to get 2.
Grab the next digit (2) from the dividend, add it to 2, then carry on: 22 / 6

Advancing to step 5:
6 can be fit into 22 3 times, resulting in a remainder of 4.
Write down 3 as next digit of the result. 
Result so far: 12973.0
Subtracting 18 from 22 leaves us with 4.
Grab the next digit (4) from the dividend, add it to 4, then carry on: 44 / 6

Advancing to step 6:
When dividing 44 by 6, we get 7 with a remainder of 2.
The next digit of our result is 7. 
Result so far: 129737.0
The remainder is 2 after subtracting 42 from 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 7:
6 goes into 20 3 times with a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 129737.3
Deduct 18 from 20 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.

Moving on to step 8:
6 can be fit into 20 3 times, resulting in a remainder of 2.
The next digit of our result is 3. 
Result so far: 129737.33
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.

In conclusion, the division gives 129737.33 with a balance of 0.002.