257413 ÷ 16 
Our goal is to divide 257413 by 16.

On to step 1:
2 divided by 16 is 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 16

Going ahead to step 2:
25 divided by 16 is 1 with a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 16 from 25 leaves us with 9.
Append the next digit (7) from the dividend to 9 and continue with: 97 / 16

Moving on to step 3:
16 can be fit into 97 6 times, resulting in a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 16.0
If we take 96 away from 97, we end up with 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 16

On to step 4:
If we divide 14 by 16, we get 0 and a remainder of 14.
The next digit of our result is 0. 
Result so far: 160.0
Subtract 0 from 14 to get 14.
Take the next digit (1) from the dividend and append it to 14, then repeat: 141 / 16

Step 5:
141 divided by 16 is 8 with a remainder of 13.
Put 8 as the next digit of the answer. 
Result so far: 1608.0
The remainder is 13 after subtracting 128 from 141.
Include the next digit (3) from the dividend after 13, then repeat: 133 / 16

Let's proceed to step 6:
The number 16 fits into 133 8 times, leaving a remainder of 5.
Record the quotient 8 as the next digit in the result. 
Result so far: 16088.0
Subtracting 128 from 133 leaves us 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 7:
When dividing 50 by 16, we get 3 with a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 16088.3
If we take 48 away from 50, we end up 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.

Moving on to step 8:
16 can be fit into 20 1 times, resulting in a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 16088.31
If we take 16 away from 20, we end up with 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 9:
If we divide 40 by 16, we get 2 and a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 16088.312
The remainder is 8 after subtracting 32 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 10:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 16088.3125
Subtracting 80 from 80 leaves us with 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 11:
0 divided by 16 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 16088.3125
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 12:
If we divide 0 by 16, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 16088.3125
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final result is 16088.3125 with a remainder of 0.0.