813030 ÷ 13 
Our goal is to divide 813030 by 13.

Moving on to step 1:
The number 13 fits into 8 0 times, leaving a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Fetch the next digit (1) from the dividend, attach it to 8 and continue: 81 / 13

Advancing to step 2:
The number 13 fits into 81 6 times, leaving a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 6.0
The remainder is 3 after subtracting 78 from 81.
Grab the next digit (3) from the dividend, add it to 3, then carry on: 33 / 13

Let's proceed to step 3:
If we divide 33 by 13, we get 2 and a remainder of 7.
The number 2 becomes the next digit in our result. 
Result so far: 62.0
If we take 26 away from 33, we end up with 7.
Take the next digit (0) from the dividend and append it to 7, then repeat: 70 / 13

Step 4:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 625.0
Deduct 65 from 70 and we're left with 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 13

Step 5:
53 divided by 13 is 4 with a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 6254.0
Subtract 52 from 53 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 13

Advancing to step 6:
If we divide 10 by 13, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 62540.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 7:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 62540.7
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 8:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 62540.76
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
13 goes into 120 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 62540.769
If we subtract 117 from 120, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 10:
30 divided by 13 is 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 62540.7692
If we subtract 26 from 30, 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.

Advancing to step 11:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 62540.76923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 12:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 62540.76923
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 13:
100 divided by 13 is 7 with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 62540.7692307
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 14:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 62540.76923076
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 62540.76923076 with a balance of 1.2e-08.