503263 divided by 6 
We're looking to find how many times 6 goes into 503263.

Step 1:
5 divided by 6 is 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 6

On to step 2:
The number 6 fits into 50 8 times, leaving a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 8.0
If we subtract 48 from 50, we get 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 6

Moving on to step 3:
6 can be fit into 23 3 times, resulting in a remainder of 5.
Record the quotient 3 as the next digit in the result. 
Result so far: 83.0
The remainder is 5 after subtracting 18 from 23.
Fetch the next digit (2) from the dividend, attach it to 5 and continue: 52 / 6

Going ahead to step 4:
When dividing 52 by 6, we get 8 with a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 838.0
If we subtract 48 from 52, we get 4.
Fetch the next digit (6) from the dividend, attach it to 4 and continue: 46 / 6

Step 5:
46 divided by 6 is 7 with a remainder of 4.
The number 7 becomes the next digit in our result. 
Result so far: 8387.0
Deduct 42 from 46 and we're left with 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Going ahead to step 6:
6 can be fit into 43 7 times, resulting in a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 83877.0
Deduct 42 from 43 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
The number 6 fits into 10 1 times, leaving a remainder of 4.
The next digit of our result is 1. 
Result so far: 83877.1
If we subtract 6 from 10, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 8:
6 can be fit into 40 6 times, resulting in a remainder of 4.
The next digit of our result is 6. 
Result so far: 83877.16
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
If we divide 40 by 6, we get 6 and a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 83877.166
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final outcome is 83877.166, with a leftover of 0.0004.