41106815 ÷ 421 
The aim is to understand the frequency of 421 in 41106815.

Going ahead to step 1:
421 can be fit into 4 0 times, resulting in a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 421

Going ahead to step 2:
The number 421 fits into 41 0 times, leaving a remainder of 41.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 41 to get 41.
Grab the next digit (1) from the dividend, add it to 41, then carry on: 411 / 421

Step 3:
When dividing 411 by 421, we get 0 with a remainder of 411.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 411, we get 411.
Grab the next digit (0) from the dividend, add it to 411, then carry on: 4110 / 421

Advancing to step 4:
4110 divided by 421 is 9 with a remainder of 321.
Put 9 as the next digit of the answer. 
Result so far: 9.0
If we subtract 3789 from 4110, we get 321.
Append the next digit (6) from the dividend to 321 and continue with: 3216 / 421

On to step 5:
When dividing 3216 by 421, we get 7 with a remainder of 269.
Use 7 as the next digit of our solution. 
Result so far: 97.0
The remainder is 269 after subtracting 2947 from 3216.
Fetch the next digit (8) from the dividend, attach it to 269 and continue: 2698 / 421

Advancing to step 6:
2698 divided by 421 is 6 with a remainder of 172.
Use 6 as the next digit of our solution. 
Result so far: 976.0
If we subtract 2526 from 2698, we get 172.
Bring next digit (1) of the dividend behind the 172 and repeat the process: 1721 / 421

Going ahead to step 7:
421 can be fit into 1721 4 times, resulting in a remainder of 37.
The number 4 becomes the next digit in our result. 
Result so far: 9764.0
If we take 1684 away from 1721, we end up with 37.
Fetch the next digit (5) from the dividend, attach it to 37 and continue: 375 / 421

Advancing to step 8:
If we divide 375 by 421, we get 0 and a remainder of 375.
Use 0 as the next digit of our solution. 
Result so far: 97640.0
The remainder is 375 after subtracting 0 from 375.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3750, and continue the process.

Moving on to step 9:
421 goes into 3750 8 times with a remainder of 382.
The number 8 becomes the next digit in our result. 
Result so far: 97640.8
The remainder is 382 after subtracting 3368 from 3750.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3820, and continue the process.

Advancing to step 10:
When dividing 3820 by 421, we get 9 with a remainder of 31.
Record the quotient 9 as the next digit in the result. 
Result so far: 97640.89
Deduct 3789 from 3820 and we're left 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.

Going ahead to step 11:
If we divide 310 by 421, we get 0 and a remainder of 310.
Use 0 as the next digit of our solution. 
Result so far: 97640.89
The remainder is 310 after subtracting 0 from 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3100, and continue the process.

Let's proceed to step 12:
421 goes into 3100 7 times with a remainder of 153.
Use 7 as the next digit of our solution. 
Result so far: 97640.8907
Subtract 2947 from 3100 to get 153.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1530, and continue the process.

Moving on to step 13:
421 can be fit into 1530 3 times, resulting in a remainder of 267.
Record the quotient 3 as the next digit in the result. 
Result so far: 97640.89073
Subtract 1263 from 1530 to get 267.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2670, and continue the process.

On to step 14:
421 can be fit into 2670 6 times, resulting in a remainder of 144.
Write down 6 as next digit of the result. 
Result so far: 97640.890736
The remainder is 144 after subtracting 2526 from 2670.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1440, and continue the process.

Advancing to step 15:
The number 421 fits into 1440 3 times, leaving a remainder of 177.
Write down 3 as next digit of the result. 
Result so far: 97640.8907363
Subtract 1263 from 1440 to get 177.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1770, and continue the process.

Step 16:
421 can be fit into 1770 4 times, resulting in a remainder of 86.
Use 4 as the next digit of our solution. 
Result so far: 97640.89073634
Subtract 1684 from 1770 to get 86.
Since there are no more digits in the dividend, we add a zero to the remainder making it 860, and continue the process.

Our division results in 97640.89073634 with a remaining 8.6e-08.