Let's divide 171966 by 41
We're looking to find how many times 41 goes into 171966.

Step 1:
If we divide 1 by 41, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 41

Advancing to step 2:
When dividing 17 by 41, we get 0 with a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Include the next digit (1) from the dividend after 17, then repeat: 171 / 41

Let's proceed to step 3:
When dividing 171 by 41, we get 4 with a remainder of 7.
Put 4 as the next digit of the answer. 
Result so far: 4.0
Deduct 164 from 171 and we're left with 7.
Fetch the next digit (9) from the dividend, attach it to 7 and continue: 79 / 41

Let's proceed to step 4:
If we divide 79 by 41, we get 1 and a remainder of 38.
Put 1 as the next digit of the answer. 
Result so far: 41.0
If we subtract 41 from 79, we get 38.
Append the next digit (6) from the dividend to 38 and continue with: 386 / 41

Moving on to step 5:
The number 41 fits into 386 9 times, leaving a remainder of 17.
The number 9 becomes the next digit in our result. 
Result so far: 419.0
Subtract 369 from 386 to get 17.
Grab the next digit (6) from the dividend, add it to 17, then carry on: 176 / 41

Step 6:
41 can be fit into 176 4 times, resulting in a remainder of 12.
Write down 4 as next digit of the result. 
Result so far: 4194.0
If we subtract 164 from 176, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 7:
If we divide 120 by 41, we get 2 and a remainder of 38.
Write down 2 as next digit of the result. 
Result so far: 4194.2
Subtracting 82 from 120 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Going ahead to step 8:
41 can be fit into 380 9 times, resulting in a remainder of 11.
The next digit of our result is 9. 
Result so far: 4194.29
If we subtract 369 from 380, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 9:
41 can be fit into 110 2 times, resulting in a remainder of 28.
The next digit of our result is 2. 
Result so far: 4194.292
If we subtract 82 from 110, we 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.

Step 10:
When dividing 280 by 41, we get 6 with a remainder of 34.
Put 6 as the next digit of the answer. 
Result so far: 4194.2926
The remainder is 34 after subtracting 246 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 11:
41 can be fit into 340 8 times, resulting in a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 4194.29268
If we take 328 away from 340, we end up 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.

Let's proceed to step 12:
120 divided by 41 is 2 with a remainder of 38.
The next digit of our result is 2. 
Result so far: 4194.292682
Deduct 82 from 120 and we're left with 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 13:
If we divide 380 by 41, we get 9 and a remainder of 11.
The next digit of our result is 9. 
Result so far: 4194.2926829
Deduct 369 from 380 and we're left with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 14:
41 can be fit into 110 2 times, resulting in a remainder of 28.
Use 2 as the next digit of our solution. 
Result so far: 4194.29268292
If we take 82 away from 110, we end up 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.

Our division results in 4194.29268292 with a remaining 2.8e-08.