Let's divide 513906 by 13
We want to divide 513906 by 13.

Step 1:
13 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 13

Let's proceed to step 2:
13 goes into 51 3 times with a remainder of 12.
The next digit of our result is 3. 
Result so far: 3.0
If we subtract 39 from 51, we get 12.
Grab the next digit (3) from the dividend, add it to 12, then carry on: 123 / 13

On to step 3:
If we divide 123 by 13, we get 9 and a remainder of 6.
Put 9 as the next digit of the answer. 
Result so far: 39.0
The remainder is 6 after subtracting 117 from 123.
Grab the next digit (9) from the dividend, add it to 6, then carry on: 69 / 13

Step 4:
69 divided by 13 is 5 with a remainder of 4.
Put 5 as the next digit of the answer. 
Result so far: 395.0
If we take 65 away from 69, we end up with 4.
Append the next digit (0) from the dividend to 4 and continue with: 40 / 13

Going ahead to step 5:
40 divided by 13 is 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 3953.0
Subtracting 39 from 40 leaves us with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 13

Let's proceed to step 6:
16 divided by 13 is 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 39531.0
If we take 13 away from 16, we end up with 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 7:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 39531.2
Subtract 26 from 30 to 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.

Moving on to step 8:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 39531.23
Subtracting 39 from 40 leaves us 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.

On to step 9:
When dividing 10 by 13, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 39531.23
If we subtract 0 from 10, we get 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 10:
100 divided by 13 is 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 39531.2307
The remainder is 9 after subtracting 91 from 100.
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 11:
13 goes into 90 6 times with a remainder of 12.
The next digit of our result is 6. 
Result so far: 39531.23076
If we take 78 away from 90, we end up 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.

Let's proceed to step 12:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 39531.230769
Subtract 117 from 120 to 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.

Step 13:
The number 13 fits into 30 2 times, leaving a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 39531.2307692
Deduct 26 from 30 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.

Step 14:
If we divide 40 by 13, we get 3 and a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 39531.23076923
Subtract 39 from 40 to 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.

After the division, we end up with 39531.23076923 and a remainder of 1e-09.