580166 ÷ 41 
The aim is to understand the frequency of 41 in 580166.

Advancing to step 1:
The number 41 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 41

Step 2:
41 goes into 58 1 times with a remainder of 17.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 17 after subtracting 41 from 58.
Include the next digit (0) from the dividend after 17, then repeat: 170 / 41

Advancing to step 3:
If we divide 170 by 41, we get 4 and a remainder of 6.
The next digit of our result is 4. 
Result so far: 14.0
Deduct 164 from 170 and we're left with 6.
Grab the next digit (1) from the dividend, add it to 6, then carry on: 61 / 41

Advancing to step 4:
41 goes into 61 1 times with a remainder of 20.
Use 1 as the next digit of our solution. 
Result so far: 141.0
Subtracting 41 from 61 leaves us with 20.
Include the next digit (6) from the dividend after 20, then repeat: 206 / 41

Moving on to step 5:
If we divide 206 by 41, we get 5 and a remainder of 1.
The next digit of our result is 5. 
Result so far: 1415.0
If we subtract 205 from 206, we get 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 41

Let's proceed to step 6:
If we divide 16 by 41, we get 0 and a remainder of 16.
Put 0 as the next digit of the answer. 
Result so far: 14150.0
Subtract 0 from 16 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 7:
160 divided by 41 is 3 with a remainder of 37.
Write down 3 as next digit of the result. 
Result so far: 14150.3
The remainder is 37 after subtracting 123 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Let's proceed to step 8:
If we divide 370 by 41, we get 9 and a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 14150.39
Deduct 369 from 370 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 9:
The number 41 fits into 10 0 times, leaving a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 14150.39
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 10:
100 divided by 41 is 2 with a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 14150.3902
Deduct 82 from 100 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 11:
The number 41 fits into 180 4 times, leaving a remainder of 16.
Put 4 as the next digit of the answer. 
Result so far: 14150.39024
Subtracting 164 from 180 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 12:
41 goes into 160 3 times with a remainder of 37.
The next digit of our result is 3. 
Result so far: 14150.390243
If we subtract 123 from 160, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 13:
The number 41 fits into 370 9 times, leaving a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 14150.3902439
Subtract 369 from 370 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 14:
41 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 14150.3902439
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 14150.3902439 and a remainder of 1e-08.