We look at the division of 256634 by 13 
The aim is to understand the frequency of 13 in 256634.

On to step 1:
When dividing 2 by 13, we get 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 13

Going ahead to step 2:
The number 13 fits into 25 1 times, leaving a remainder of 12.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 13 away from 25, we end up with 12.
Take the next digit (6) from the dividend and append it to 12, then repeat: 126 / 13

On to step 3:
If we divide 126 by 13, we get 9 and a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 19.0
Subtracting 117 from 126 leaves us with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 13

Moving on to step 4:
13 can be fit into 96 7 times, resulting in a remainder of 5.
Use 7 as the next digit of our solution. 
Result so far: 197.0
If we take 91 away from 96, we end up with 5.
Fetch the next digit (3) from the dividend, attach it to 5 and continue: 53 / 13

Step 5:
When dividing 53 by 13, we get 4 with a remainder of 1.
Use 4 as the next digit of our solution. 
Result so far: 1974.0
If we take 52 away from 53, we end up with 1.
Include the next digit (4) from the dividend after 1, then repeat: 14 / 13

Step 6:
14 divided by 13 is 1 with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 19741.0
If we take 13 away from 14, 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 7:
If we divide 10 by 13, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 19741.0
The remainder is 10 after subtracting 0 from 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 8:
If we divide 100 by 13, we get 7 and a remainder of 9.
The next digit of our result is 7. 
Result so far: 19741.07
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.

Moving on to step 9:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 19741.076
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.

Moving on to step 10:
120 divided by 13 is 9 with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 19741.0769
Subtract 117 from 120 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.

Step 11:
If we divide 30 by 13, we get 2 and a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 19741.07692
If we take 26 away from 30, we end up 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 12:
If we divide 40 by 13, we get 3 and a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 19741.076923
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 13:
If we divide 10 by 13, we get 0 and a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 19741.076923
Subtract 0 from 10 to 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 14:
100 divided by 13 is 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 19741.07692307
If we subtract 91 from 100, we 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.

The final result is 19741.07692307 with a remainder of 9e-09.