563697 divided by 41 
The aim is to understand the frequency of 41 in 563697.

Advancing to step 1:
5 divided by 41 is 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 41

Let's proceed to step 2:
If we divide 56 by 41, we get 1 and a remainder of 15.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 41 from 56 leaves us with 15.
Take the next digit (3) from the dividend and append it to 15, then repeat: 153 / 41

Going ahead to step 3:
41 goes into 153 3 times with a remainder of 30.
The next digit of our result is 3. 
Result so far: 13.0
Subtracting 123 from 153 leaves us with 30.
Bring next digit (6) of the dividend behind the 30 and repeat the process: 306 / 41

Advancing to step 4:
If we divide 306 by 41, we get 7 and a remainder of 19.
Record the quotient 7 as the next digit in the result. 
Result so far: 137.0
Subtract 287 from 306 to get 19.
Append the next digit (9) from the dividend to 19 and continue with: 199 / 41

Going ahead to step 5:
41 goes into 199 4 times with a remainder of 35.
The next digit of our result is 4. 
Result so far: 1374.0
The remainder is 35 after subtracting 164 from 199.
Fetch the next digit (7) from the dividend, attach it to 35 and continue: 357 / 41

Let's proceed to step 6:
357 divided by 41 is 8 with a remainder of 29.
Use 8 as the next digit of our solution. 
Result so far: 13748.0
The remainder is 29 after subtracting 328 from 357.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Advancing to step 7:
If we divide 290 by 41, we get 7 and a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 13748.7
Deduct 287 from 290 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 8:
30 divided by 41 is 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 13748.7
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 9:
300 divided by 41 is 7 with a remainder of 13.
Write down 7 as next digit of the result. 
Result so far: 13748.707
Deduct 287 from 300 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 10:
41 goes into 130 3 times with a remainder of 7.
The next digit of our result is 3. 
Result so far: 13748.7073
Deduct 123 from 130 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 11:
41 can be fit into 70 1 times, resulting in a remainder of 29.
Put 1 as the next digit of the answer. 
Result so far: 13748.70731
Deduct 41 from 70 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

On to step 12:
When dividing 290 by 41, we get 7 with a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 13748.707317
If we subtract 287 from 290, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 13:
If we divide 30 by 41, we get 0 and a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 13748.707317
Deduct 0 from 30 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 14:
The number 41 fits into 300 7 times, leaving a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 13748.70731707
Subtracting 287 from 300 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The final outcome is 13748.70731707, with a leftover of 1.3e-08.