We look at the division of 512315 by 13 
We want to divide 512315 by 13.

On to step 1:
5 divided by 13 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 13

Going ahead to step 2:
If we divide 51 by 13, we get 3 and a remainder of 12.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Deduct 39 from 51 and we're left with 12.
Append the next digit (2) from the dividend to 12 and continue with: 122 / 13

Advancing to step 3:
The number 13 fits into 122 9 times, leaving a remainder of 5.
Put 9 as the next digit of the answer. 
Result so far: 39.0
Subtracting 117 from 122 leaves us with 5.
Include the next digit (3) from the dividend after 5, then repeat: 53 / 13

Going ahead to step 4:
53 divided by 13 is 4 with a remainder of 1.
The next digit of our result is 4. 
Result so far: 394.0
If we take 52 away from 53, we end up with 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 13

Let's proceed to step 5:
13 goes into 11 0 times with a remainder of 11.
Write down 0 as next digit of the result. 
Result so far: 3940.0
Subtracting 0 from 11 leaves us with 11.
Append the next digit (5) from the dividend to 11 and continue with: 115 / 13

Advancing to step 6:
If we divide 115 by 13, we get 8 and a remainder of 11.
The next digit of our result is 8. 
Result so far: 39408.0
Deduct 104 from 115 and we're left with 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 7:
110 divided by 13 is 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 39408.8
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 8:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 39408.84
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 9:
13 goes into 80 6 times with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 39408.846
If we take 78 away from 80, we end up 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.

Step 10:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 39408.8461
Deduct 13 from 20 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 11:
If we divide 70 by 13, we get 5 and a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 39408.84615
If we take 65 away from 70, we end up with 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 12:
50 divided by 13 is 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 39408.846153
Subtracting 39 from 50 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 13:
If we divide 110 by 13, we get 8 and a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 39408.8461538
Deduct 104 from 110 and we're left 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.

Advancing to step 14:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 39408.84615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

After the division, we end up with 39408.84615384 and a remainder of 8e-09.