105872 ÷ 82 
Our goal is to divide 105872 by 82.

On to step 1:
When dividing 1 by 82, we get 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 82

Advancing to step 2:
If we divide 10 by 82, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 82

Let's proceed to step 3:
The number 82 fits into 105 1 times, leaving a remainder of 23.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 82 from 105 leaves us with 23.
Take the next digit (8) from the dividend and append it to 23, then repeat: 238 / 82

Step 4:
If we divide 238 by 82, we get 2 and a remainder of 74.
The next digit of our result is 2. 
Result so far: 12.0
If we subtract 164 from 238, we get 74.
Fetch the next digit (7) from the dividend, attach it to 74 and continue: 747 / 82

On to step 5:
747 divided by 82 is 9 with a remainder of 9.
The next digit of our result is 9. 
Result so far: 129.0
If we take 738 away from 747, we end up with 9.
Bring next digit (2) of the dividend behind the 9 and repeat the process: 92 / 82

Going ahead to step 6:
82 can be fit into 92 1 times, resulting in a remainder of 10.
The next digit of our result is 1. 
Result so far: 1291.0
Subtract 82 from 92 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.

Moving on to step 7:
82 goes into 100 1 times with a remainder of 18.
Use 1 as the next digit of our solution. 
Result so far: 1291.1
If we take 82 away from 100, we end up 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.

Going ahead to step 8:
If we divide 180 by 82, we get 2 and a remainder of 16.
Write down 2 as next digit of the result. 
Result so far: 1291.12
If we subtract 164 from 180, we get 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 9:
82 goes into 160 1 times with a remainder of 78.
Record the quotient 1 as the next digit in the result. 
Result so far: 1291.121
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.

On to step 10:
When dividing 780 by 82, we get 9 with a remainder of 42.
Put 9 as the next digit of the answer. 
Result so far: 1291.1219
Subtracting 738 from 780 leaves us 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.

Going ahead to step 11:
If we divide 420 by 82, we get 5 and a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 1291.12195
The remainder is 10 after subtracting 410 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 12:
82 can be fit into 100 1 times, resulting in a remainder of 18.
Use 1 as the next digit of our solution. 
Result so far: 1291.121951
Deduct 82 from 100 and we're left 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.

Going ahead to step 13:
180 divided by 82 is 2 with a remainder of 16.
Put 2 as the next digit of the answer. 
Result so far: 1291.1219512
Subtracting 164 from 180 leaves us 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.

Moving on to step 14:
The number 82 fits into 160 1 times, leaving a remainder of 78.
Use 1 as the next digit of our solution. 
Result so far: 1291.12195121
Deduct 82 from 160 and we're left with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

The final outcome is 1291.12195121, with a leftover of 7.8e-08.