109817 divided by 41 
We want to figure out the number of times 109817 can be divided by 41.

Step 1:
1 divided by 41 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 41

On to step 2:
The number 41 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Append the next digit (9) from the dividend to 10 and continue with: 109 / 41

Step 3:
The number 41 fits into 109 2 times, leaving a remainder of 27.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we take 82 away from 109, we end up with 27.
Grab the next digit (8) from the dividend, add it to 27, then carry on: 278 / 41

Advancing to step 4:
41 goes into 278 6 times with a remainder of 32.
The number 6 becomes the next digit in our result. 
Result so far: 26.0
Subtract 246 from 278 to get 32.
Take the next digit (1) from the dividend and append it to 32, then repeat: 321 / 41

Moving on to step 5:
If we divide 321 by 41, we get 7 and a remainder of 34.
Put 7 as the next digit of the answer. 
Result so far: 267.0
If we subtract 287 from 321, we get 34.
Append the next digit (7) from the dividend to 34 and continue with: 347 / 41

On to step 6:
When dividing 347 by 41, we get 8 with a remainder of 19.
Record the quotient 8 as the next digit in the result. 
Result so far: 2678.0
Subtracting 328 from 347 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 7:
If we divide 190 by 41, we get 4 and a remainder of 26.
Put 4 as the next digit of the answer. 
Result so far: 2678.4
Subtracting 164 from 190 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 8:
41 goes into 260 6 times with a remainder of 14.
Record the quotient 6 as the next digit in the result. 
Result so far: 2678.46
If we subtract 246 from 260, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 9:
41 can be fit into 140 3 times, resulting in a remainder of 17.
The next digit of our result is 3. 
Result so far: 2678.463
Subtract 123 from 140 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 10:
The number 41 fits into 170 4 times, leaving a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 2678.4634
The remainder is 6 after subtracting 164 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 11:
41 goes into 60 1 times with a remainder of 19.
Write down 1 as next digit of the result. 
Result so far: 2678.46341
If we take 41 away from 60, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 12:
41 goes into 190 4 times with a remainder of 26.
The number 4 becomes the next digit in our result. 
Result so far: 2678.463414
If we subtract 164 from 190, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Going ahead to step 13:
When dividing 260 by 41, we get 6 with a remainder of 14.
Record the quotient 6 as the next digit in the result. 
Result so far: 2678.4634146
Subtract 246 from 260 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 14:
If we divide 140 by 41, we get 3 and a remainder of 17.
Use 3 as the next digit of our solution. 
Result so far: 2678.46341463
Deduct 123 from 140 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 2678.46341463 and a remainder of 1.7e-08.