We look at the division of 565165 by 13 
The aim is to understand the frequency of 13 in 565165.

Advancing to step 1:
5 divided by 13 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 13

Step 2:
The number 13 fits into 56 4 times, leaving a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 52 from 56 and we're left with 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 13

Moving on to step 3:
When dividing 45 by 13, we get 3 with a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 43.0
If we take 39 away from 45, we end up with 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 13

Step 4:
13 goes into 61 4 times with a remainder of 9.
Write down 4 as next digit of the result. 
Result so far: 434.0
Subtracting 52 from 61 leaves us with 9.
Append the next digit (6) from the dividend to 9 and continue with: 96 / 13

Advancing to step 5:
13 goes into 96 7 times with a remainder of 5.
The next digit of our result is 7. 
Result so far: 4347.0
The remainder is 5 after subtracting 91 from 96.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 13

Moving on to step 6:
55 divided by 13 is 4 with a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 43474.0
Subtract 52 from 55 to 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.

Moving on to step 7:
30 divided by 13 is 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 43474.2
Deduct 26 from 30 and we're left 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.

Advancing to step 8:
40 divided by 13 is 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 43474.23
If we take 39 away from 40, we end up 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:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 43474.23
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
100 divided by 13 is 7 with a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 43474.2307
Subtract 91 from 100 to get 9.
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:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 43474.23076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 12:
13 can be fit into 120 9 times, resulting in a remainder of 3.
The next digit of our result is 9. 
Result so far: 43474.230769
Deduct 117 from 120 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.

Let's proceed to step 13:
13 can be fit into 30 2 times, resulting in a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 43474.2307692
If we subtract 26 from 30, 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.

Step 14:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 43474.23076923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 43474.23076923 and a remainder of 1e-09.