We look at the division of 11457 by 13 
The aim is to understand the frequency of 13 in 11457.

Going ahead to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 13

Advancing to step 2:
If we divide 11 by 13, we get 0 and a remainder of 11.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 11 leaves us with 11.
Bring next digit (4) of the dividend behind the 11 and repeat the process: 114 / 13

Step 3:
The number 13 fits into 114 8 times, leaving a remainder of 10.
Put 8 as the next digit of the answer. 
Result so far: 8.0
If we take 104 away from 114, we end up with 10.
Include the next digit (5) from the dividend after 10, then repeat: 105 / 13

Advancing to step 4:
13 goes into 105 8 times with a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 88.0
Subtract 104 from 105 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 13

On to step 5:
17 divided by 13 is 1 with a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 881.0
Subtracting 13 from 17 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.

Let's proceed to step 6:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 881.3
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.

Going ahead to step 7:
If we divide 10 by 13, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 881.3
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.

Let's proceed to step 8:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 881.307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 881.3076
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:
13 goes into 120 9 times with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 881.30769
Subtracting 117 from 120 leaves us 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.

Going ahead to step 11:
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: 881.307692
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 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: 881.3076923
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.

Going ahead 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: 881.3076923
If we take 0 away from 10, we end up 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.

Our division results in 881.3076923 with a remaining 1e-08.