We're dividing 13657 by 41 
The aim is to understand the frequency of 41 in 13657.

Step 1:
41 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 41

Going ahead to step 2:
41 can be fit into 13 0 times, resulting in a remainder of 13.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Fetch the next digit (6) from the dividend, attach it to 13 and continue: 136 / 41

Moving on to step 3:
The number 41 fits into 136 3 times, leaving a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 123 from 136, we get 13.
Take the next digit (5) from the dividend and append it to 13, then repeat: 135 / 41

Let's proceed to step 4:
41 goes into 135 3 times with a remainder of 12.
The next digit of our result is 3. 
Result so far: 33.0
Deduct 123 from 135 and we're left with 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 41

On to step 5:
When dividing 127 by 41, we get 3 with a remainder of 4.
The next digit of our result is 3. 
Result so far: 333.0
If we subtract 123 from 127, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 6:
41 goes into 40 0 times with a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 333.0
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 7:
41 can be fit into 400 9 times, resulting in a remainder of 31.
Record the quotient 9 as the next digit in the result. 
Result so far: 333.09
Subtract 369 from 400 to get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 8:
The number 41 fits into 310 7 times, leaving a remainder of 23.
Use 7 as the next digit of our solution. 
Result so far: 333.097
If we take 287 away from 310, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 9:
The number 41 fits into 230 5 times, leaving a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 333.0975
Deduct 205 from 230 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 10:
41 can be fit into 250 6 times, resulting in a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 333.09756
Subtracting 246 from 250 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 11:
The number 41 fits into 40 0 times, leaving a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 333.09756
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 12:
41 can be fit into 400 9 times, resulting in a remainder of 31.
The number 9 becomes the next digit in our result. 
Result so far: 333.0975609
If we take 369 away from 400, we end up 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.

Advancing to step 13:
The number 41 fits into 310 7 times, leaving a remainder of 23.
Record the quotient 7 as the next digit in the result. 
Result so far: 333.09756097
Subtracting 287 from 310 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

The final outcome is 333.09756097, with a leftover of 2.3e-08.