We're dividing 557181 by 41 
The aim is to understand the frequency of 41 in 557181.

Step 1:
41 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 41

On to step 2:
The number 41 fits into 55 1 times, leaving a remainder of 14.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 41 from 55 leaves us with 14.
Take the next digit (7) from the dividend and append it to 14, then repeat: 147 / 41

Let's proceed to step 3:
41 goes into 147 3 times with a remainder of 24.
Use 3 as the next digit of our solution. 
Result so far: 13.0
If we take 123 away from 147, we end up with 24.
Include the next digit (1) from the dividend after 24, then repeat: 241 / 41

Going ahead to step 4:
41 can be fit into 241 5 times, resulting in a remainder of 36.
The number 5 becomes the next digit in our result. 
Result so far: 135.0
Deduct 205 from 241 and we're left with 36.
Fetch the next digit (8) from the dividend, attach it to 36 and continue: 368 / 41

Moving on to step 5:
If we divide 368 by 41, we get 8 and a remainder of 40.
Use 8 as the next digit of our solution. 
Result so far: 1358.0
Subtracting 328 from 368 leaves us with 40.
Take the next digit (1) from the dividend and append it to 40, then repeat: 401 / 41

On to step 6:
401 divided by 41 is 9 with a remainder of 32.
Record the quotient 9 as the next digit in the result. 
Result so far: 13589.0
The remainder is 32 after subtracting 369 from 401.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 7:
If we divide 320 by 41, we get 7 and a remainder of 33.
The next digit of our result is 7. 
Result so far: 13589.7
Subtract 287 from 320 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.

Going ahead to step 8:
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: 13589.78
Deduct 328 from 330 and we're left 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.

Step 9:
41 can be fit into 20 0 times, resulting in a remainder of 20.
The next digit of our result is 0. 
Result so far: 13589.78
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 10:
When dividing 200 by 41, we get 4 with a remainder of 36.
Put 4 as the next digit of the answer. 
Result so far: 13589.7804
The remainder is 36 after subtracting 164 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 11:
360 divided by 41 is 8 with a remainder of 32.
The number 8 becomes the next digit in our result. 
Result so far: 13589.78048
The remainder is 32 after subtracting 328 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 12:
320 divided by 41 is 7 with a remainder of 33.
Put 7 as the next digit of the answer. 
Result so far: 13589.780487
The remainder is 33 after subtracting 287 from 320.
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 13:
41 goes into 330 8 times with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 13589.7804878
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.

Going ahead to step 14:
When dividing 20 by 41, we get 0 with a remainder of 20.
The next digit of our result is 0. 
Result so far: 13589.7804878
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.

After the division, we end up with 13589.7804878 and a remainder of 2e-08.