We're dividing 645209 by 6 
We want to divide 645209 by 6.

Advancing to step 1:
6 divided by 6 is 1 with a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 6 away from 6, we end up with 0.
Append the next digit (4) from the dividend to 0 and continue with: 4 / 6

Going ahead to step 2:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 10.0
If we take 0 away from 4, we end up with 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 6

Step 3:
When dividing 45 by 6, we get 7 with a remainder of 3.
The next digit of our result is 7. 
Result so far: 107.0
If we subtract 42 from 45, we get 3.
Append the next digit (2) from the dividend to 3 and continue with: 32 / 6

Moving on to step 4:
6 can be fit into 32 5 times, resulting in a remainder of 2.
The number 5 becomes the next digit in our result. 
Result so far: 1075.0
If we take 30 away from 32, we end up with 2.
Grab the next digit (0) from the dividend, add it to 2, then carry on: 20 / 6

Advancing to step 5:
6 can be fit into 20 3 times, resulting in a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 10753.0
If we subtract 18 from 20, we get 2.
Append the next digit (9) from the dividend to 2 and continue with: 29 / 6

Moving on to step 6:
When dividing 29 by 6, we get 4 with a remainder of 5.
Use 4 as the next digit of our solution. 
Result so far: 107534.0
If we subtract 24 from 29, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
6 goes into 50 8 times with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 107534.8
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.

On to step 8:
When dividing 20 by 6, we get 3 with a remainder of 2.
The next digit of our result is 3. 
Result so far: 107534.83
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.

Moving on to step 9:
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: 107534.833
If we subtract 18 from 20, we 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.

The final result is 107534.833 with a remainder of 0.0002.