102771 divided by 13 
The aim is to understand the frequency of 13 in 102771.

Step 1:
1 divided by 13 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

Advancing to step 2:
13 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Fetch the next digit (2) from the dividend, attach it to 10 and continue: 102 / 13

Let's proceed to step 3:
13 can be fit into 102 7 times, resulting in a remainder of 11.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtracting 91 from 102 leaves us with 11.
Fetch the next digit (7) from the dividend, attach it to 11 and continue: 117 / 13

Let's proceed to step 4:
13 goes into 117 9 times with a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 79.0
Subtracting 117 from 117 leaves us with 0.
Take the next digit (7) from the dividend and append it to 0, then repeat: 7 / 13

Going ahead to step 5:
7 divided by 13 is 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 790.0
Subtract 0 from 7 to get 7.
Grab the next digit (1) from the dividend, add it to 7, then carry on: 71 / 13

Advancing to step 6:
When dividing 71 by 13, we get 5 with a remainder of 6.
Record the quotient 5 as the next digit in the result. 
Result so far: 7905.0
If we subtract 65 from 71, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
When dividing 60 by 13, we get 4 with a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 7905.4
Deduct 52 from 60 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 8:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 7905.46
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 9:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 7905.461
Deduct 13 from 20 and we're left 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.

Moving on to step 10:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 7905.4615
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.

Advancing to step 11:
50 divided by 13 is 3 with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 7905.46153
Subtract 39 from 50 to 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.

Let's proceed to step 12:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 7905.461538
Deduct 104 from 110 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 13:
13 can be fit into 60 4 times, resulting in a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 7905.4615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 14:
13 can be fit into 80 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 7905.46153846
Subtract 78 from 80 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The final result is 7905.46153846 with a remainder of 2e-09.