81782 ÷ 12 
We're looking to find how many times 12 goes into 81782.

Let's proceed to step 1:
12 goes into 8 0 times with a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 12

Moving on to step 2:
12 can be fit into 81 6 times, resulting in a remainder of 9.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 72 from 81 to get 9.
Append the next digit (7) from the dividend to 9 and continue with: 97 / 12

Step 3:
The number 12 fits into 97 8 times, leaving a remainder of 1.
The next digit of our result is 8. 
Result so far: 68.0
Subtracting 96 from 97 leaves us with 1.
Grab the next digit (8) from the dividend, add it to 1, then carry on: 18 / 12

On to step 4:
12 can be fit into 18 1 times, resulting in a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 681.0
Subtracting 12 from 18 leaves us with 6.
Grab the next digit (2) from the dividend, add it to 6, then carry on: 62 / 12

Going ahead to step 5:
If we divide 62 by 12, we get 5 and a remainder of 2.
The number 5 becomes the next digit in our result. 
Result so far: 6815.0
Subtract 60 from 62 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 6:
If we divide 20 by 12, we get 1 and a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 6815.1
If we subtract 12 from 20, 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.

Let's proceed to step 7:
12 can be fit into 80 6 times, resulting in a remainder of 8.
The next digit of our result is 6. 
Result so far: 6815.16
The remainder is 8 after subtracting 72 from 80.
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 8:
If we divide 80 by 12, we get 6 and a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 6815.166
Deduct 72 from 80 and we're left 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.

In conclusion, the division gives 6815.166 with a balance of 0.0008.