We're dividing 257583 by 13 
Let's see how many times 13 fits into 257583.

On to step 1:
13 goes into 2 0 times with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 13

Advancing to step 2:
13 goes into 25 1 times with a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 13 away from 25, we end up with 12.
Take the next digit (7) from the dividend and append it to 12, then repeat: 127 / 13

Advancing to step 3:
The number 13 fits into 127 9 times, leaving a remainder of 10.
The next digit of our result is 9. 
Result so far: 19.0
Subtract 117 from 127 to get 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 13

Step 4:
105 divided by 13 is 8 with a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 198.0
If we take 104 away from 105, we end up with 1.
Grab the next digit (8) from the dividend, add it to 1, then carry on: 18 / 13

Moving on to step 5:
18 divided by 13 is 1 with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 1981.0
If we subtract 13 from 18, we get 5.
Append the next digit (3) from the dividend to 5 and continue with: 53 / 13

Advancing to step 6:
53 divided by 13 is 4 with a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 19814.0
Subtracting 52 from 53 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.

Step 7:
If we divide 10 by 13, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 19814.0
Subtracting 0 from 10 leaves us 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 8:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 19814.07
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 9:
When dividing 90 by 13, we get 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 19814.076
Subtract 78 from 90 to get 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 10:
13 goes into 120 9 times with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 19814.0769
Deduct 117 from 120 and we're left 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.

Going ahead to step 11:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 19814.07692
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.

Let's proceed to step 12:
40 divided by 13 is 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 19814.076923
If we subtract 39 from 40, we 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.

On to step 13:
10 divided by 13 is 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 19814.076923
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.

On to step 14:
When dividing 100 by 13, we get 7 with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 19814.07692307
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

The final result is 19814.07692307 with a remainder of 9e-09.