157575 ÷ 41 
The aim is to understand the frequency of 41 in 157575.

Let's proceed to step 1:
1 divided by 41 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 41

Moving on to step 2:
41 goes into 15 0 times with a remainder of 15.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 15 to get 15.
Include the next digit (7) from the dividend after 15, then repeat: 157 / 41

Going ahead to step 3:
157 divided by 41 is 3 with a remainder of 34.
The next digit of our result is 3. 
Result so far: 3.0
Subtracting 123 from 157 leaves us with 34.
Append the next digit (5) from the dividend to 34 and continue with: 345 / 41

On to step 4:
The number 41 fits into 345 8 times, leaving a remainder of 17.
Record the quotient 8 as the next digit in the result. 
Result so far: 38.0
Deduct 328 from 345 and we're left with 17.
Append the next digit (7) from the dividend to 17 and continue with: 177 / 41

Going ahead to step 5:
The number 41 fits into 177 4 times, leaving a remainder of 13.
Put 4 as the next digit of the answer. 
Result so far: 384.0
The remainder is 13 after subtracting 164 from 177.
Include the next digit (5) from the dividend after 13, then repeat: 135 / 41

Let's proceed to step 6:
41 goes into 135 3 times with a remainder of 12.
Record the quotient 3 as the next digit in the result. 
Result so far: 3843.0
The remainder is 12 after subtracting 123 from 135.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 7:
41 goes into 120 2 times with a remainder of 38.
Put 2 as the next digit of the answer. 
Result so far: 3843.2
If we take 82 away from 120, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 8:
The number 41 fits into 380 9 times, leaving a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 3843.29
Subtract 369 from 380 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 9:
41 goes into 110 2 times with a remainder of 28.
Write down 2 as next digit of the result. 
Result so far: 3843.292
If we subtract 82 from 110, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 10:
41 can be fit into 280 6 times, resulting in a remainder of 34.
Write down 6 as next digit of the result. 
Result so far: 3843.2926
If we subtract 246 from 280, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 11:
If we divide 340 by 41, we get 8 and a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 3843.29268
Deduct 328 from 340 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 12:
When dividing 120 by 41, we get 2 with a remainder of 38.
The number 2 becomes the next digit in our result. 
Result so far: 3843.292682
Deduct 82 from 120 and we're left with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Step 13:
When dividing 380 by 41, we get 9 with a remainder of 11.
Write down 9 as next digit of the result. 
Result so far: 3843.2926829
Subtracting 369 from 380 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 14:
When dividing 110 by 41, we get 2 with a remainder of 28.
The next digit of our result is 2. 
Result so far: 3843.29268292
Subtracting 82 from 110 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

The final result is 3843.29268292 with a remainder of 2.8e-08.