166165 ÷ 41 
We want to figure out the number of times 166165 can be divided by 41.

Advancing to step 1:
If we divide 1 by 41, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 41

Moving on to step 2:
41 can be fit into 16 0 times, resulting in a remainder of 16.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 16 and we're left with 16.
Append the next digit (6) from the dividend to 16 and continue with: 166 / 41

Step 3:
The number 41 fits into 166 4 times, leaving a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtracting 164 from 166 leaves us with 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 41

Moving on to step 4:
41 can be fit into 21 0 times, resulting in a remainder of 21.
Use 0 as the next digit of our solution. 
Result so far: 40.0
Subtracting 0 from 21 leaves us with 21.
Take the next digit (6) from the dividend and append it to 21, then repeat: 216 / 41

Advancing to step 5:
The number 41 fits into 216 5 times, leaving a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 405.0
Deduct 205 from 216 and we're left with 11.
Append the next digit (5) from the dividend to 11 and continue with: 115 / 41

Moving on to step 6:
If we divide 115 by 41, we get 2 and a remainder of 33.
The number 2 becomes the next digit in our result. 
Result so far: 4052.0
Subtract 82 from 115 to get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 7:
41 can be fit into 330 8 times, resulting in a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 4052.8
Subtracting 328 from 330 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
41 can be fit into 20 0 times, resulting in a remainder of 20.
Record the quotient 0 as the next digit in the result. 
Result so far: 4052.8
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
When dividing 200 by 41, we get 4 with a remainder of 36.
The next digit of our result is 4. 
Result so far: 4052.804
Deduct 164 from 200 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 10:
41 can be fit into 360 8 times, resulting in a remainder of 32.
The next digit of our result is 8. 
Result so far: 4052.8048
Subtract 328 from 360 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 11:
The number 41 fits into 320 7 times, leaving a remainder of 33.
The number 7 becomes the next digit in our result. 
Result so far: 4052.80487
If we subtract 287 from 320, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

On to step 12:
41 goes into 330 8 times with a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 4052.804878
Subtracting 328 from 330 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 13:
41 can be fit into 20 0 times, resulting in a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 4052.804878
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 14:
The number 41 fits into 200 4 times, leaving a remainder of 36.
Write down 4 as next digit of the result. 
Result so far: 4052.80487804
Deduct 164 from 200 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

After the division, we end up with 4052.80487804 and a remainder of 3.6e-08.