135844 ÷ 82 
Our goal is to divide 135844 by 82.

On to step 1:
The number 82 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 82

Step 2:
The number 82 fits into 13 0 times, leaving a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 13, we end up with 13.
Include the next digit (5) from the dividend after 13, then repeat: 135 / 82

On to step 3:
82 can be fit into 135 1 times, resulting in a remainder of 53.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 82 away from 135, we end up with 53.
Append the next digit (8) from the dividend to 53 and continue with: 538 / 82

On to step 4:
82 goes into 538 6 times with a remainder of 46.
Put 6 as the next digit of the answer. 
Result so far: 16.0
Subtract 492 from 538 to get 46.
Include the next digit (4) from the dividend after 46, then repeat: 464 / 82

Let's proceed to step 5:
The number 82 fits into 464 5 times, leaving a remainder of 54.
Put 5 as the next digit of the answer. 
Result so far: 165.0
The remainder is 54 after subtracting 410 from 464.
Include the next digit (4) from the dividend after 54, then repeat: 544 / 82

Step 6:
544 divided by 82 is 6 with a remainder of 52.
The number 6 becomes the next digit in our result. 
Result so far: 1656.0
Subtracting 492 from 544 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 7:
520 divided by 82 is 6 with a remainder of 28.
The number 6 becomes the next digit in our result. 
Result so far: 1656.6
Subtract 492 from 520 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 8:
The number 82 fits into 280 3 times, leaving a remainder of 34.
Write down 3 as next digit of the result. 
Result so far: 1656.63
Deduct 246 from 280 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 9:
The number 82 fits into 340 4 times, leaving a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 1656.634
Deduct 328 from 340 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 10:
82 goes into 120 1 times with a remainder of 38.
Use 1 as the next digit of our solution. 
Result so far: 1656.6341
If we subtract 82 from 120, we get 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Let's proceed to step 11:
380 divided by 82 is 4 with a remainder of 52.
Write down 4 as next digit of the result. 
Result so far: 1656.63414
If we take 328 away from 380, we end up with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Advancing to step 12:
If we divide 520 by 82, we get 6 and a remainder of 28.
Write down 6 as next digit of the result. 
Result so far: 1656.634146
Deduct 492 from 520 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 13:
The number 82 fits into 280 3 times, leaving a remainder of 34.
The number 3 becomes the next digit in our result. 
Result so far: 1656.6341463
Subtract 246 from 280 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 14:
82 goes into 340 4 times with a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 1656.63414634
Deduct 328 from 340 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

After the division, we end up with 1656.63414634 and a remainder of 1.2e-08.