We're dividing 4157 by 82 
We're looking to find how many times 82 goes into 4157.

Step 1:
If we divide 4 by 82, we get 0 and a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 82

On to step 2:
If we divide 41 by 82, we get 0 and a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 41, we end up with 41.
Take the next digit (5) from the dividend and append it to 41, then repeat: 415 / 82

Step 3:
If we divide 415 by 82, we get 5 and a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 5.0
Deduct 410 from 415 and we're left with 5.
Append the next digit (7) from the dividend to 5 and continue with: 57 / 82

On to step 4:
82 can be fit into 57 0 times, resulting in a remainder of 57.
Write down 0 as next digit of the result. 
Result so far: 50.0
Subtract 0 from 57 to get 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Let's proceed to step 5:
82 goes into 570 6 times with a remainder of 78.
Use 6 as the next digit of our solution. 
Result so far: 50.6
The remainder is 78 after subtracting 492 from 570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Let's proceed to step 6:
When dividing 780 by 82, we get 9 with a remainder of 42.
Write down 9 as next digit of the result. 
Result so far: 50.69
Subtract 738 from 780 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 7:
If we divide 420 by 82, we get 5 and a remainder of 10.
The next digit of our result is 5. 
Result so far: 50.695
Subtract 410 from 420 to 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.

Let's proceed to step 8:
100 divided by 82 is 1 with a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 50.6951
Subtracting 82 from 100 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 9:
82 goes into 180 2 times with a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 50.69512
Deduct 164 from 180 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 10:
160 divided by 82 is 1 with a remainder of 78.
Record the quotient 1 as the next digit in the result. 
Result so far: 50.695121
If we subtract 82 from 160, we get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Going ahead to step 11:
82 can be fit into 780 9 times, resulting in a remainder of 42.
Write down 9 as next digit of the result. 
Result so far: 50.6951219
If we take 738 away from 780, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

On to step 12:
The number 82 fits into 420 5 times, leaving a remainder of 10.
The next digit of our result is 5. 
Result so far: 50.69512195
Subtracting 410 from 420 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.

In conclusion, the division gives 50.69512195 with a balance of 1e-08.