We divide 412345 by 41
The aim is to understand the frequency of 41 in 412345.

Advancing to step 1:
When dividing 4 by 41, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 41

On to step 2:
If we divide 41 by 41, we get 1 and a remainder of 0.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 41 from 41 and we're left with 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 41

Let's proceed to step 3:
41 can be fit into 2 0 times, resulting in a remainder of 2.
The next digit of our result is 0. 
Result so far: 10.0
If we subtract 0 from 2, we get 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 41

Going ahead to step 4:
41 goes into 23 0 times with a remainder of 23.
The next digit of our result is 0. 
Result so far: 100.0
Deduct 0 from 23 and we're left with 23.
Include the next digit (4) from the dividend after 23, then repeat: 234 / 41

On to step 5:
The number 41 fits into 234 5 times, leaving a remainder of 29.
The number 5 becomes the next digit in our result. 
Result so far: 1005.0
If we subtract 205 from 234, we get 29.
Take the next digit (5) from the dividend and append it to 29, then repeat: 295 / 41

Advancing to step 6:
The number 41 fits into 295 7 times, leaving a remainder of 8.
The next digit of our result is 7. 
Result so far: 10057.0
If we take 287 away from 295, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 7:
41 goes into 80 1 times with a remainder of 39.
The next digit of our result is 1. 
Result so far: 10057.1
The remainder is 39 after subtracting 41 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 8:
If we divide 390 by 41, we get 9 and a remainder of 21.
The number 9 becomes the next digit in our result. 
Result so far: 10057.19
The remainder is 21 after subtracting 369 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Step 9:
The number 41 fits into 210 5 times, leaving a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 10057.195
Subtract 205 from 210 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 10:
The number 41 fits into 50 1 times, leaving a remainder of 9.
The next digit of our result is 1. 
Result so far: 10057.1951
The remainder is 9 after subtracting 41 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 11:
41 can be fit into 90 2 times, resulting in a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 10057.19512
Subtract 82 from 90 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 12:
The number 41 fits into 80 1 times, leaving a remainder of 39.
Use 1 as the next digit of our solution. 
Result so far: 10057.195121
If we subtract 41 from 80, we get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Moving on to step 13:
41 can be fit into 390 9 times, resulting in a remainder of 21.
The next digit of our result is 9. 
Result so far: 10057.1951219
The remainder is 21 after subtracting 369 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 14:
The number 41 fits into 210 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 10057.19512195
If we take 205 away from 210, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 10057.19512195, and the remainder is 5e-09.