We look at the division of 109506 by 13 
The aim is to understand the frequency of 13 in 109506.

Let's proceed 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
If we subtract 0 from 1, we get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 13

Advancing to step 2:
When dividing 10 by 13, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Append the next digit (9) from the dividend to 10 and continue with: 109 / 13

Going ahead to step 3:
109 divided by 13 is 8 with a remainder of 5.
Write down 8 as next digit of the result. 
Result so far: 8.0
Subtracting 104 from 109 leaves us with 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 13

Going ahead to step 4:
If we divide 55 by 13, we get 4 and a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 84.0
The remainder is 3 after subtracting 52 from 55.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 13

Let's proceed to step 5:
13 goes into 30 2 times with a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 842.0
Subtract 26 from 30 to get 4.
Fetch the next digit (6) from the dividend, attach it to 4 and continue: 46 / 13

Advancing to step 6:
46 divided by 13 is 3 with a remainder of 7.
The next digit of our result is 3. 
Result so far: 8423.0
Subtracting 39 from 46 leaves us 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.

Step 7:
13 can be fit into 70 5 times, resulting in a remainder of 5.
The next digit of our result is 5. 
Result so far: 8423.5
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
13 goes into 50 3 times with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 8423.53
The remainder is 11 after subtracting 39 from 50.
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:
When dividing 110 by 13, we get 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 8423.538
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 10:
When dividing 60 by 13, we get 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 8423.5384
If we subtract 52 from 60, we 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.

Going ahead to step 11:
13 goes into 80 6 times with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 8423.53846
If we take 78 away from 80, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 12:
When dividing 20 by 13, we get 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 8423.538461
If we take 13 away from 20, we end up 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.

Going ahead to step 13:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 8423.5384615
Subtracting 65 from 70 leaves us 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.

Moving on to step 14:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 8423.53846153
If we subtract 39 from 50, we 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.

The final outcome is 8423.53846153, with a leftover of 1.1e-08.