We're dividing 81721 by 41 
We want to figure out the number of times 81721 can be divided by 41.

Advancing to step 1:
The number 41 fits into 8 0 times, leaving 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 / 41

Moving on to step 2:
41 goes into 81 1 times with a remainder of 40.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 41 away from 81, we end up with 40.
Grab the next digit (7) from the dividend, add it to 40, then carry on: 407 / 41

Moving on to step 3:
The number 41 fits into 407 9 times, leaving a remainder of 38.
Put 9 as the next digit of the answer. 
Result so far: 19.0
The remainder is 38 after subtracting 369 from 407.
Grab the next digit (2) from the dividend, add it to 38, then carry on: 382 / 41

On to step 4:
When dividing 382 by 41, we get 9 with a remainder of 13.
The number 9 becomes the next digit in our result. 
Result so far: 199.0
Subtract 369 from 382 to get 13.
Bring next digit (1) of the dividend behind the 13 and repeat the process: 131 / 41

On to step 5:
The number 41 fits into 131 3 times, leaving a remainder of 8.
The number 3 becomes the next digit in our result. 
Result so far: 1993.0
Subtracting 123 from 131 leaves us 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.

Going ahead to step 6:
41 can be fit into 80 1 times, resulting in a remainder of 39.
Use 1 as the next digit of our solution. 
Result so far: 1993.1
If we take 41 away from 80, we end up with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Step 7:
The number 41 fits into 390 9 times, leaving a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 1993.19
Deduct 369 from 390 and we're left with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Let's proceed to step 8:
41 goes into 210 5 times with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 1993.195
If we subtract 205 from 210, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 9:
If we divide 50 by 41, we get 1 and a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 1993.1951
Deduct 41 from 50 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 10:
90 divided by 41 is 2 with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 1993.19512
Subtracting 82 from 90 leaves us 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.

On to step 11:
80 divided by 41 is 1 with a remainder of 39.
Put 1 as the next digit of the answer. 
Result so far: 1993.195121
The remainder is 39 after subtracting 41 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 12:
The number 41 fits into 390 9 times, leaving a remainder of 21.
The next digit of our result is 9. 
Result so far: 1993.1951219
Subtracting 369 from 390 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Let's proceed to step 13:
The number 41 fits into 210 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 1993.19512195
If we subtract 205 from 210, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 1993.19512195, and the remainder is 5e-09.