We look at the division of 779138 by 6 
We're looking to find how many times 6 goes into 779138.

Step 1:
6 goes into 7 1 times with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 6 from 7 and we're left with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 6

On to step 2:
6 can be fit into 17 2 times, resulting in a remainder of 5.
Write down 2 as next digit of the result. 
Result so far: 12.0
Subtract 12 from 17 to get 5.
Grab the next digit (9) from the dividend, add it to 5, then carry on: 59 / 6

Let's proceed to step 3:
59 divided by 6 is 9 with a remainder of 5.
The number 9 becomes the next digit in our result. 
Result so far: 129.0
Subtracting 54 from 59 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 6

On to step 4:
When dividing 51 by 6, we get 8 with a remainder of 3.
The next digit of our result is 8. 
Result so far: 1298.0
Deduct 48 from 51 and we're left with 3.
Include the next digit (3) from the dividend after 3, then repeat: 33 / 6

Step 5:
When dividing 33 by 6, we get 5 with a remainder of 3.
The next digit of our result is 5. 
Result so far: 12985.0
If we subtract 30 from 33, we get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 6:
38 divided by 6 is 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 129856.0
Subtracting 36 from 38 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.

On to step 7:
6 goes into 20 3 times with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 129856.3
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.

Step 8:
If we divide 20 by 6, we get 3 and a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 129856.33
If we take 18 away from 20, we end up 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.

The final outcome is 129856.33, with a leftover of 0.002.