We're dividing 257205 by 13 
We're looking to find how many times 13 goes into 257205.

Step 1:
13 goes into 2 0 times with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 13

Let's proceed to step 2:
13 can be fit into 25 1 times, resulting in a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 12 after subtracting 13 from 25.
Bring next digit (7) of the dividend behind the 12 and repeat the process: 127 / 13

On to step 3:
When dividing 127 by 13, we get 9 with a remainder of 10.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
Deduct 117 from 127 and we're left with 10.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 13

Step 4:
If we divide 102 by 13, we get 7 and a remainder of 11.
Put 7 as the next digit of the answer. 
Result so far: 197.0
Subtracting 91 from 102 leaves us with 11.
Fetch the next digit (0) from the dividend, attach it to 11 and continue: 110 / 13

On to step 5:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 1978.0
Deduct 104 from 110 and we're left with 6.
Append the next digit (5) from the dividend to 6 and continue with: 65 / 13

Let's proceed to step 6:
When dividing 65 by 13, we get 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 19785.0
Subtract 65 from 65 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 7:
The number 13 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 19785.0
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 8:
0 divided by 13 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 19785.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 19785.0 with a balance of 0.0.