83080 ÷ 13 
The aim is to understand the frequency of 13 in 83080.

On to step 1:
If we divide 8 by 13, we get 0 and a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Fetch the next digit (3) from the dividend, attach it to 8 and continue: 83 / 13

Advancing to step 2:
13 goes into 83 6 times with a remainder of 5.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 78 from 83 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 13

Step 3:
13 can be fit into 50 3 times, resulting in a remainder of 11.
Record the quotient 3 as the next digit in the result. 
Result so far: 63.0
If we take 39 away from 50, we end up with 11.
Bring next digit (8) of the dividend behind the 11 and repeat the process: 118 / 13

On to step 4:
The number 13 fits into 118 9 times, leaving a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 639.0
Deduct 117 from 118 and we're left with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 13

Advancing to step 5:
10 divided by 13 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 6390.0
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.

Step 6:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 6390.7
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 7:
The number 13 fits into 90 6 times, leaving a remainder of 12.
The next digit of our result is 6. 
Result so far: 6390.76
If we subtract 78 from 90, we 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.

On to step 8:
When dividing 120 by 13, we get 9 with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 6390.769
If we take 117 away from 120, we end up 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.

On to step 9:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 6390.7692
Subtracting 26 from 30 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.

Going ahead to step 10:
When dividing 40 by 13, we get 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 6390.76923
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.

Step 11:
13 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 6390.76923
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.

Let's proceed to step 12:
When dividing 100 by 13, we get 7 with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 6390.7692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 13:
When dividing 90 by 13, we get 6 with a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 6390.76923076
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.

The final result is 6390.76923076 with a remainder of 1.2e-08.