Let's divide 81682 by 97
We want to figure out the number of times 81682 can be divided by 97.

Advancing to step 1:
97 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 8 leaves us with 8.
Fetch the next digit (1) from the dividend, attach it to 8 and continue: 81 / 97

Moving on to step 2:
97 goes into 81 0 times with a remainder of 81.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 81 after subtracting 0 from 81.
Take the next digit (6) from the dividend and append it to 81, then repeat: 816 / 97

On to step 3:
The number 97 fits into 816 8 times, leaving a remainder of 40.
Write down 8 as next digit of the result. 
Result so far: 8.0
Subtracting 776 from 816 leaves us with 40.
Include the next digit (8) from the dividend after 40, then repeat: 408 / 97

On to step 4:
97 can be fit into 408 4 times, resulting in a remainder of 20.
Use 4 as the next digit of our solution. 
Result so far: 84.0
If we subtract 388 from 408, we get 20.
Append the next digit (2) from the dividend to 20 and continue with: 202 / 97

Going ahead to step 5:
97 goes into 202 2 times with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 842.0
If we subtract 194 from 202, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 6:
The number 97 fits into 80 0 times, leaving a remainder of 80.
The next digit of our result is 0. 
Result so far: 842.0
Subtracting 0 from 80 leaves us with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 7:
If we divide 800 by 97, we get 8 and a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 842.08
Subtract 776 from 800 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 8:
240 divided by 97 is 2 with a remainder of 46.
Put 2 as the next digit of the answer. 
Result so far: 842.082
Subtract 194 from 240 to get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 9:
97 can be fit into 460 4 times, resulting in a remainder of 72.
The number 4 becomes the next digit in our result. 
Result so far: 842.0824
Subtract 388 from 460 to get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Advancing to step 10:
The number 97 fits into 720 7 times, leaving a remainder of 41.
Write down 7 as next digit of the result. 
Result so far: 842.08247
Subtract 679 from 720 to get 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 11:
97 can be fit into 410 4 times, resulting in a remainder of 22.
Record the quotient 4 as the next digit in the result. 
Result so far: 842.082474
Deduct 388 from 410 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 12:
97 goes into 220 2 times with a remainder of 26.
Record the quotient 2 as the next digit in the result. 
Result so far: 842.0824742
If we subtract 194 from 220, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Step 13:
97 goes into 260 2 times with a remainder of 66.
Write down 2 as next digit of the result. 
Result so far: 842.08247422
Deduct 194 from 260 and we're left with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

The final result is 842.08247422 with a remainder of 6.6e-08.