We're dividing 21674 by 82 
We're looking to find how many times 82 goes into 21674.

Moving on to step 1:
If we divide 2 by 82, we get 0 and a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 82

Moving on to step 2:
If we divide 21 by 82, we get 0 and a remainder of 21.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 21 to get 21.
Include the next digit (6) from the dividend after 21, then repeat: 216 / 82

Step 3:
When dividing 216 by 82, we get 2 with a remainder of 52.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtracting 164 from 216 leaves us with 52.
Append the next digit (7) from the dividend to 52 and continue with: 527 / 82

Moving on to step 4:
The number 82 fits into 527 6 times, leaving a remainder of 35.
Use 6 as the next digit of our solution. 
Result so far: 26.0
Deduct 492 from 527 and we're left with 35.
Bring next digit (4) of the dividend behind the 35 and repeat the process: 354 / 82

Let's proceed to step 5:
When dividing 354 by 82, we get 4 with a remainder of 26.
Use 4 as the next digit of our solution. 
Result so far: 264.0
The remainder is 26 after subtracting 328 from 354.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 6:
260 divided by 82 is 3 with a remainder of 14.
The next digit of our result is 3. 
Result so far: 264.3
The remainder is 14 after subtracting 246 from 260.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
82 goes into 140 1 times with a remainder of 58.
Use 1 as the next digit of our solution. 
Result so far: 264.31
The remainder is 58 after subtracting 82 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 8:
580 divided by 82 is 7 with a remainder of 6.
The number 7 becomes the next digit in our result. 
Result so far: 264.317
If we subtract 574 from 580, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 9:
When dividing 60 by 82, we get 0 with a remainder of 60.
Use 0 as the next digit of our solution. 
Result so far: 264.317
Deduct 0 from 60 and we're left with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 10:
If we divide 600 by 82, we get 7 and a remainder of 26.
The next digit of our result is 7. 
Result so far: 264.31707
If we take 574 away from 600, we end up with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 11:
The number 82 fits into 260 3 times, leaving a remainder of 14.
Write down 3 as next digit of the result. 
Result so far: 264.317073
Deduct 246 from 260 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 12:
82 goes into 140 1 times with a remainder of 58.
Put 1 as the next digit of the answer. 
Result so far: 264.3170731
The remainder is 58 after subtracting 82 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 13:
82 can be fit into 580 7 times, resulting in a remainder of 6.
The number 7 becomes the next digit in our result. 
Result so far: 264.31707317
The remainder is 6 after subtracting 574 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 264.31707317 and a remainder of 6e-09.