We look at the division of 257172 by 13 
Our goal is to divide 257172 by 13.

Advancing to step 1:
2 divided by 13 is 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 13

Moving on to step 2:
25 divided by 13 is 1 with a remainder of 12.
Use 1 as the next digit of our solution. 
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

Let's proceed to step 3:
If we divide 127 by 13, we get 9 and a remainder of 10.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
If we take 117 away from 127, we end up with 10.
Take the next digit (1) from the dividend and append it to 10, then repeat: 101 / 13

Advancing to step 4:
When dividing 101 by 13, we get 7 with a remainder of 10.
The number 7 becomes the next digit in our result. 
Result so far: 197.0
Subtract 91 from 101 to get 10.
Bring next digit (7) of the dividend behind the 10 and repeat the process: 107 / 13

Advancing to step 5:
13 goes into 107 8 times with a remainder of 3.
Put 8 as the next digit of the answer. 
Result so far: 1978.0
Subtract 104 from 107 to get 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 13

Moving on to step 6:
The number 13 fits into 32 2 times, leaving a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 19782.0
If we subtract 26 from 32, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 7:
When dividing 60 by 13, we get 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 19782.4
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.

Advancing to step 8:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 19782.46
Deduct 78 from 80 and we're left 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.

Let's proceed to step 9:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 19782.461
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.

Let's proceed to step 10:
70 divided by 13 is 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 19782.4615
If we subtract 65 from 70, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
When dividing 50 by 13, we get 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 19782.46153
Deduct 39 from 50 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 12:
110 divided by 13 is 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 19782.461538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 13:
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: 19782.4615384
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.

Moving on to step 14:
13 goes into 80 6 times with a remainder of 2.
The next digit of our result is 6. 
Result so far: 19782.46153846
Subtract 78 from 80 to 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.

The quotient of the division is 19782.46153846, and the remainder is 2e-09.