108666 ÷ 41 
We want to figure out the number of times 108666 can be divided by 41.

On to 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
If we subtract 0 from 1, we get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 41

Step 2:
The number 41 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Fetch the next digit (8) from the dividend, attach it to 10 and continue: 108 / 41

On to step 3:
41 can be fit into 108 2 times, resulting in a remainder of 26.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we subtract 82 from 108, we get 26.
Grab the next digit (6) from the dividend, add it to 26, then carry on: 266 / 41

Advancing to step 4:
When dividing 266 by 41, we get 6 with a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 26.0
The remainder is 20 after subtracting 246 from 266.
Take the next digit (6) from the dividend and append it to 20, then repeat: 206 / 41

Let's proceed to step 5:
When dividing 206 by 41, we get 5 with a remainder of 1.
The next digit of our result is 5. 
Result so far: 265.0
Subtracting 205 from 206 leaves us with 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 41

Let's proceed to step 6:
The number 41 fits into 16 0 times, leaving a remainder of 16.
The next digit of our result is 0. 
Result so far: 2650.0
If we take 0 away from 16, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 7:
41 can be fit into 160 3 times, resulting in a remainder of 37.
Put 3 as the next digit of the answer. 
Result so far: 2650.3
If we take 123 away from 160, we end up with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Moving on to step 8:
370 divided by 41 is 9 with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 2650.39
Deduct 369 from 370 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 9:
10 divided by 41 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 2650.39
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
100 divided by 41 is 2 with a remainder of 18.
Put 2 as the next digit of the answer. 
Result so far: 2650.3902
Subtracting 82 from 100 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 11:
41 goes into 180 4 times with a remainder of 16.
Use 4 as the next digit of our solution. 
Result so far: 2650.39024
Deduct 164 from 180 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 12:
When dividing 160 by 41, we get 3 with a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 2650.390243
The remainder is 37 after subtracting 123 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 13:
If we divide 370 by 41, we get 9 and a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 2650.3902439
If we subtract 369 from 370, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 14:
The number 41 fits into 10 0 times, leaving a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 2650.3902439
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Our division results in 2650.3902439 with a remaining 1e-08.