21105 divided by 41 
We want to figure out the number of times 21105 can be divided by 41.

Going ahead to step 1:
The number 41 fits into 2 0 times, leaving a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 41

Step 2:
The number 41 fits into 21 0 times, leaving a remainder of 21.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 21, we end up with 21.
Append the next digit (1) from the dividend to 21 and continue with: 211 / 41

On to step 3:
41 can be fit into 211 5 times, resulting in a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 205 from 211 leaves us with 6.
Append the next digit (0) from the dividend to 6 and continue with: 60 / 41

Advancing to step 4:
When dividing 60 by 41, we get 1 with a remainder of 19.
The number 1 becomes the next digit in our result. 
Result so far: 51.0
Subtract 41 from 60 to get 19.
Fetch the next digit (5) from the dividend, attach it to 19 and continue: 195 / 41

Advancing to step 5:
If we divide 195 by 41, we get 4 and a remainder of 31.
Write down 4 as next digit of the result. 
Result so far: 514.0
Subtracting 164 from 195 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 6:
41 goes into 310 7 times with a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 514.7
If we subtract 287 from 310, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 7:
If we divide 230 by 41, we get 5 and a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 514.75
Deduct 205 from 230 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
When dividing 250 by 41, we get 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 514.756
If we subtract 246 from 250, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
41 goes into 40 0 times with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 514.756
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 10:
The number 41 fits into 400 9 times, leaving a remainder of 31.
The next digit of our result is 9. 
Result so far: 514.75609
The remainder is 31 after subtracting 369 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 11:
41 goes into 310 7 times with a remainder of 23.
Use 7 as the next digit of our solution. 
Result so far: 514.756097
Deduct 287 from 310 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 12:
41 goes into 230 5 times with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 514.7560975
Subtracting 205 from 230 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 13:
41 goes into 250 6 times with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 514.75609756
If we subtract 246 from 250, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

After the division, we end up with 514.75609756 and a remainder of 4e-09.