812539 ÷ 13 
Our goal is to divide 812539 by 13.

Moving on to step 1:
13 can be fit into 8 0 times, resulting in a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Bring next digit (1) of the dividend behind the 8 and repeat the process: 81 / 13

Moving on to step 2:
If we divide 81 by 13, we get 6 and a remainder of 3.
The next digit of our result is 6. 
Result so far: 6.0
If we take 78 away from 81, we end up with 3.
Bring next digit (2) of the dividend behind the 3 and repeat the process: 32 / 13

On to step 3:
13 can be fit into 32 2 times, resulting in a remainder of 6.
The next digit of our result is 2. 
Result so far: 62.0
If we subtract 26 from 32, we get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 13

Moving on to step 4:
65 divided by 13 is 5 with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 625.0
Subtract 65 from 65 to get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 13

Advancing to step 5:
3 divided by 13 is 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 6250.0
If we subtract 0 from 3, we get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 13

On to step 6:
The number 13 fits into 39 3 times, leaving a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 62503.0
Deduct 39 from 39 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 7:
13 can be fit into 0 0 times, resulting in a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 62503.0
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
When dividing 0 by 13, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 62503.0
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 62503.0, with a leftover of 0.0.