We're dividing 82102 by 16 
We're looking to find how many times 16 goes into 82102.

Advancing to step 1:
16 can be fit into 8 0 times, resulting in a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Include the next digit (2) from the dividend after 8, then repeat: 82 / 16

Moving on to step 2:
The number 16 fits into 82 5 times, leaving a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtract 80 from 82 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 16

Moving on to step 3:
21 divided by 16 is 1 with a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 51.0
Deduct 16 from 21 and we're left with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 16

On to step 4:
The number 16 fits into 50 3 times, leaving a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 513.0
Deduct 48 from 50 and we're left with 2.
Include the next digit (2) from the dividend after 2, then repeat: 22 / 16

Advancing to step 5:
16 goes into 22 1 times with a remainder of 6.
The next digit of our result is 1. 
Result so far: 5131.0
Subtracting 16 from 22 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 6:
16 goes into 60 3 times with a remainder of 12.
Record the quotient 3 as the next digit in the result. 
Result so far: 5131.3
If we subtract 48 from 60, we 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.

Let's proceed to step 7:
16 can be fit into 120 7 times, resulting in a remainder of 8.
Use 7 as the next digit of our solution. 
Result so far: 5131.37
If we take 112 away from 120, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 8:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 5131.375
If we take 80 away from 80, 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.

Moving on to step 9:
If we divide 0 by 16, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 5131.375
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.

Let's proceed to step 10:
0 divided by 16 is 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 5131.375
The remainder is 0 after subtracting 0 from 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 5131.375 with a remainder of 0.0.