257841 ÷ 13 
Let's see how many times 13 fits into 257841.

Going ahead to step 1:
13 goes into 2 0 times with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 13

Let's proceed to step 2:
If we divide 25 by 13, we get 1 and a remainder of 12.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 13 from 25 leaves us with 12.
Append the next digit (7) from the dividend to 12 and continue with: 127 / 13

Advancing to step 3:
If we divide 127 by 13, we get 9 and a remainder of 10.
Write down 9 as next digit of the result. 
Result so far: 19.0
Deduct 117 from 127 and we're left with 10.
Fetch the next digit (8) from the dividend, attach it to 10 and continue: 108 / 13

Step 4:
108 divided by 13 is 8 with a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 198.0
Subtract 104 from 108 to get 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 13

Going ahead to step 5:
If we divide 44 by 13, we get 3 and a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 1983.0
Subtract 39 from 44 to get 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 13

Step 6:
51 divided by 13 is 3 with a remainder of 12.
Write down 3 as next digit of the result. 
Result so far: 19833.0
If we take 39 away from 51, 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.

Moving on to step 7:
When dividing 120 by 13, we get 9 with a remainder of 3.
The next digit of our result is 9. 
Result so far: 19833.9
If we subtract 117 from 120, we 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.

On to step 8:
If we divide 30 by 13, we get 2 and a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 19833.92
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 19833.923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 10:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 19833.923
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 11:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 19833.92307
Subtract 91 from 100 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 12:
13 goes into 90 6 times with a remainder of 12.
The next digit of our result is 6. 
Result so far: 19833.923076
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.

Step 13:
If we divide 120 by 13, we get 9 and a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 19833.9230769
If we take 117 away from 120, 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 14:
13 goes into 30 2 times with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 19833.92307692
If we subtract 26 from 30, we 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.

Our division results in 19833.92307692 with a remaining 4e-09.