196641 divided by 13 
The aim is to understand the frequency of 13 in 196641.

On to step 1:
When dividing 1 by 13, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 13

Moving on to step 2:
13 goes into 19 1 times with a remainder of 6.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 13 away from 19, we end up with 6.
Fetch the next digit (6) from the dividend, attach it to 6 and continue: 66 / 13

Moving on to step 3:
66 divided by 13 is 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 15.0
The remainder is 1 after subtracting 65 from 66.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 13

Step 4:
13 goes into 16 1 times with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 151.0
If we subtract 13 from 16, we get 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 13

Going ahead to step 5:
If we divide 34 by 13, we get 2 and a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 1512.0
Subtract 26 from 34 to get 8.
Fetch the next digit (1) from the dividend, attach it to 8 and continue: 81 / 13

Step 6:
When dividing 81 by 13, we get 6 with a remainder of 3.
Write down 6 as next digit of the result. 
Result so far: 15126.0
If we subtract 78 from 81, 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.

Advancing to step 7:
13 can be fit into 30 2 times, resulting in a remainder of 4.
The next digit of our result is 2. 
Result so far: 15126.2
Subtracting 26 from 30 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 8:
When dividing 40 by 13, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 15126.23
Deduct 39 from 40 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.

Moving on to step 9:
13 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 15126.23
Subtracting 0 from 10 leaves us 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.

Advancing to step 10:
When dividing 100 by 13, we get 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 15126.2307
If we take 91 away from 100, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 11:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 15126.23076
If we take 78 away from 90, we end up 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.

Going ahead to step 12:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 15126.230769
If we subtract 117 from 120, 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.

Going ahead to step 13:
If we divide 30 by 13, we get 2 and a remainder of 4.
The next digit of our result is 2. 
Result so far: 15126.2307692
Subtracting 26 from 30 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.

Step 14:
13 goes into 40 3 times with a remainder of 1.
The next digit of our result is 3. 
Result so far: 15126.23076923
Subtracting 39 from 40 leaves us 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.

In conclusion, the division gives 15126.23076923 with a balance of 1e-09.