We're dividing 639677 by 6 
Let's see how many times 6 fits into 639677.

Going ahead to step 1:
6 can be fit into 6 1 times, resulting in a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 6 from 6 to get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 6

Moving on to step 2:
When dividing 3 by 6, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we subtract 0 from 3, we get 3.
Grab the next digit (9) from the dividend, add it to 3, then carry on: 39 / 6

Let's proceed to step 3:
6 goes into 39 6 times with a remainder of 3.
The next digit of our result is 6. 
Result so far: 106.0
If we take 36 away from 39, we end up with 3.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 6

Step 4:
36 divided by 6 is 6 with a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 1066.0
Subtracting 36 from 36 leaves us with 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 6

Step 5:
6 can be fit into 7 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 10661.0
Subtract 6 from 7 to get 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 6

Advancing to step 6:
If we divide 17 by 6, we get 2 and a remainder of 5.
Use 2 as the next digit of our solution. 
Result so far: 106612.0
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.

On to step 7:
6 can be fit into 50 8 times, resulting in a remainder of 2.
The next digit of our result is 8. 
Result so far: 106612.8
Subtracting 48 from 50 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.

Advancing to step 8:
20 divided by 6 is 3 with a remainder of 2.
Put 3 as the next digit of the answer. 
Result so far: 106612.83
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.

Let's proceed to step 9:
The number 6 fits into 20 3 times, leaving a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 106612.833
Subtract 18 from 20 to get 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 106612.833 with a balance of 0.0002.