819564 ÷ 41 
The aim is to understand the frequency of 41 in 819564.

On to step 1:
When dividing 8 by 41, we get 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 41

On to step 2:
When dividing 81 by 41, we get 1 with a remainder of 40.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 41 away from 81, we end up with 40.
Include the next digit (9) from the dividend after 40, then repeat: 409 / 41

On to step 3:
If we divide 409 by 41, we get 9 and a remainder of 40.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
Deduct 369 from 409 and we're left with 40.
Grab the next digit (5) from the dividend, add it to 40, then carry on: 405 / 41

Going ahead to step 4:
41 goes into 405 9 times with a remainder of 36.
Write down 9 as next digit of the result. 
Result so far: 199.0
Subtracting 369 from 405 leaves us with 36.
Take the next digit (6) from the dividend and append it to 36, then repeat: 366 / 41

Going ahead to step 5:
The number 41 fits into 366 8 times, leaving a remainder of 38.
Record the quotient 8 as the next digit in the result. 
Result so far: 1998.0
Deduct 328 from 366 and we're left with 38.
Fetch the next digit (4) from the dividend, attach it to 38 and continue: 384 / 41

Step 6:
41 goes into 384 9 times with a remainder of 15.
Put 9 as the next digit of the answer. 
Result so far: 19989.0
If we take 369 away from 384, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 7:
When dividing 150 by 41, we get 3 with a remainder of 27.
The next digit of our result is 3. 
Result so far: 19989.3
Subtracting 123 from 150 leaves us with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 8:
If we divide 270 by 41, we get 6 and a remainder of 24.
The next digit of our result is 6. 
Result so far: 19989.36
If we take 246 away from 270, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 9:
When dividing 240 by 41, we get 5 with a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 19989.365
If we take 205 away from 240, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 10:
41 can be fit into 350 8 times, resulting in a remainder of 22.
Write down 8 as next digit of the result. 
Result so far: 19989.3658
Subtracting 328 from 350 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 11:
When dividing 220 by 41, we get 5 with a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 19989.36585
If we subtract 205 from 220, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 12:
150 divided by 41 is 3 with a remainder of 27.
Use 3 as the next digit of our solution. 
Result so far: 19989.365853
Deduct 123 from 150 and we're left with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Let's proceed to step 13:
The number 41 fits into 270 6 times, leaving a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 19989.3658536
Deduct 246 from 270 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 14:
When dividing 240 by 41, we get 5 with a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 19989.36585365
The remainder is 35 after subtracting 205 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The final result is 19989.36585365 with a remainder of 3.5e-08.