We look at the division of 457102 by 871 
Our goal is to divide 457102 by 871.

Step 1:
When dividing 4 by 871, we get 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 871

Moving on to step 2:
871 can be fit into 45 0 times, resulting in a remainder of 45.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 45 and we're left with 45.
Take the next digit (7) from the dividend and append it to 45, then repeat: 457 / 871

Advancing to step 3:
When dividing 457 by 871, we get 0 with a remainder of 457.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 457, we end up with 457.
Append the next digit (1) from the dividend to 457 and continue with: 4571 / 871

Step 4:
If we divide 4571 by 871, we get 5 and a remainder of 216.
Put 5 as the next digit of the answer. 
Result so far: 5.0
The remainder is 216 after subtracting 4355 from 4571.
Include the next digit (0) from the dividend after 216, then repeat: 2160 / 871

On to step 5:
If we divide 2160 by 871, we get 2 and a remainder of 418.
Write down 2 as next digit of the result. 
Result so far: 52.0
The remainder is 418 after subtracting 1742 from 2160.
Include the next digit (2) from the dividend after 418, then repeat: 4182 / 871

Let's proceed to step 6:
If we divide 4182 by 871, we get 4 and a remainder of 698.
Use 4 as the next digit of our solution. 
Result so far: 524.0
If we subtract 3484 from 4182, we get 698.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6980, and continue the process.

Let's proceed to step 7:
871 goes into 6980 8 times with a remainder of 12.
The next digit of our result is 8. 
Result so far: 524.8
Subtract 6968 from 6980 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.

Moving on to step 8:
The number 871 fits into 120 0 times, leaving a remainder of 120.
Use 0 as the next digit of our solution. 
Result so far: 524.8
The remainder is 120 after subtracting 0 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1200, and continue the process.

Going ahead to step 9:
871 can be fit into 1200 1 times, resulting in a remainder of 329.
Use 1 as the next digit of our solution. 
Result so far: 524.801
Subtract 871 from 1200 to get 329.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3290, and continue the process.

Going ahead to step 10:
The number 871 fits into 3290 3 times, leaving a remainder of 677.
Record the quotient 3 as the next digit in the result. 
Result so far: 524.8013
Subtracting 2613 from 3290 leaves us with 677.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6770, and continue the process.

On to step 11:
If we divide 6770 by 871, we get 7 and a remainder of 673.
Use 7 as the next digit of our solution. 
Result so far: 524.80137
If we take 6097 away from 6770, we end up with 673.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6730, and continue the process.

Moving on to step 12:
871 goes into 6730 7 times with a remainder of 633.
The number 7 becomes the next digit in our result. 
Result so far: 524.801377
Deduct 6097 from 6730 and we're left with 633.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6330, and continue the process.

The final result is 524.801377 with a remainder of 6.33e-05.