We look at the division of 506774 by 13 
We want to divide 506774 by 13.

Advancing to step 1:
13 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 13

On to step 2:
13 goes into 50 3 times with a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 39 from 50, we get 11.
Append the next digit (6) from the dividend to 11 and continue with: 116 / 13

Let's proceed to step 3:
If we divide 116 by 13, we get 8 and a remainder of 12.
The next digit of our result is 8. 
Result so far: 38.0
Subtracting 104 from 116 leaves us with 12.
Fetch the next digit (7) from the dividend, attach it to 12 and continue: 127 / 13

On to step 4:
13 goes into 127 9 times with a remainder of 10.
The number 9 becomes the next digit in our result. 
Result so far: 389.0
Subtracting 117 from 127 leaves us with 10.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 13

Advancing to step 5:
The number 13 fits into 107 8 times, leaving a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 3898.0
The remainder is 3 after subtracting 104 from 107.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 13

Going ahead to step 6:
13 goes into 34 2 times with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 38982.0
If we take 26 away from 34, we end up 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.

Advancing to step 7:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 38982.6
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 38982.61
Subtract 13 from 20 to 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.

On to step 9:
70 divided by 13 is 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 38982.615
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 10:
The number 13 fits into 50 3 times, leaving a remainder of 11.
The next digit of our result is 3. 
Result so far: 38982.6153
The remainder is 11 after subtracting 39 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 11:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 38982.61538
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.

Let's proceed to step 12:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 38982.615384
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 13:
80 divided by 13 is 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 38982.6153846
Subtracting 78 from 80 leaves us 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 14:
When dividing 20 by 13, we get 1 with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 38982.61538461
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.

The final outcome is 38982.61538461, with a leftover of 7e-09.