We look at the division of 503309 by 6 
We want to figure out the number of times 503309 can be divided by 6.

On to step 1:
When dividing 5 by 6, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 6

On to step 2:
If we divide 50 by 6, we get 8 and a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Subtracting 48 from 50 leaves us with 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 6

Step 3:
When dividing 23 by 6, we get 3 with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 83.0
The remainder is 5 after subtracting 18 from 23.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 6

Advancing to step 4:
6 goes into 53 8 times with a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 838.0
Subtracting 48 from 53 leaves us with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 6

Going ahead to step 5:
6 goes into 50 8 times with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 8388.0
If we take 48 away from 50, we end up with 2.
Append the next digit (9) from the dividend to 2 and continue with: 29 / 6

Going ahead to step 6:
6 goes into 29 4 times with a remainder of 5.
Record the quotient 4 as the next digit in the result. 
Result so far: 83884.0
Subtracting 24 from 29 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.

Advancing to step 7:
When dividing 50 by 6, we get 8 with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 83884.8
Subtract 48 from 50 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.

On to step 8:
20 divided by 6 is 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 83884.83
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.

Let's proceed to step 9:
If we divide 20 by 6, we get 3 and a remainder of 2.
The next digit of our result is 3. 
Result so far: 83884.833
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 quotient of the division is 83884.833, and the remainder is 0.0002.