We look at the division of 513791 by 13 
We want to figure out the number of times 513791 can be divided by 13.

Step 1:
5 divided by 13 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 13

Moving on to step 2:
13 goes into 51 3 times with a remainder of 12.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 39 from 51, we get 12.
Take the next digit (3) from the dividend and append it to 12, then repeat: 123 / 13

Going ahead to step 3:
13 can be fit into 123 9 times, resulting in a remainder of 6.
The number 9 becomes the next digit in our result. 
Result so far: 39.0
Subtract 117 from 123 to get 6.
Grab the next digit (7) from the dividend, add it to 6, then carry on: 67 / 13

On to step 4:
If we divide 67 by 13, we get 5 and a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 395.0
If we subtract 65 from 67, we get 2.
Fetch the next digit (9) from the dividend, attach it to 2 and continue: 29 / 13

On to step 5:
If we divide 29 by 13, we get 2 and a remainder of 3.
Write down 2 as next digit of the result. 
Result so far: 3952.0
Subtract 26 from 29 to get 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 13

On to step 6:
31 divided by 13 is 2 with a remainder of 5.
The number 2 becomes the next digit in our result. 
Result so far: 39522.0
Subtract 26 from 31 to 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.

Going ahead to step 7:
If we divide 50 by 13, we get 3 and a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 39522.3
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 8:
If we divide 110 by 13, we get 8 and a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 39522.38
Subtracting 104 from 110 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 9:
If we divide 60 by 13, we get 4 and a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 39522.384
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 10:
80 divided by 13 is 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 39522.3846
Deduct 78 from 80 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.

On to step 11:
13 goes into 20 1 times with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 39522.38461
If we subtract 13 from 20, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 12:
The number 13 fits into 70 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 39522.384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 13:
50 divided by 13 is 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 39522.3846153
Subtract 39 from 50 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 14:
110 divided by 13 is 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 39522.38461538
Subtract 104 from 110 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Our division results in 39522.38461538 with a remaining 6e-09.