289962 ÷ 13 
The aim is to understand the frequency of 13 in 289962.

On to step 1:
When dividing 2 by 13, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 13

Step 2:
When dividing 28 by 13, we get 2 with a remainder of 2.
The next digit of our result is 2. 
Result so far: 2.0
The remainder is 2 after subtracting 26 from 28.
Take the next digit (9) from the dividend and append it to 2, then repeat: 29 / 13

Advancing to step 3:
The number 13 fits into 29 2 times, leaving a remainder of 3.
The number 2 becomes the next digit in our result. 
Result so far: 22.0
Deduct 26 from 29 and we're left with 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 13

Moving on to step 4:
13 goes into 39 3 times with a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 223.0
The remainder is 0 after subtracting 39 from 39.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 13

Going ahead to step 5:
13 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 2230.0
Deduct 0 from 6 and we're left with 6.
Include the next digit (2) from the dividend after 6, then repeat: 62 / 13

Let's proceed to step 6:
13 can be fit into 62 4 times, resulting in a remainder of 10.
The number 4 becomes the next digit in our result. 
Result so far: 22304.0
If we take 52 away from 62, 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.

Advancing to step 7:
If we divide 100 by 13, we get 7 and a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 22304.7
If we take 91 away from 100, we end up 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.

Going ahead to step 8:
13 goes into 90 6 times with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 22304.76
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.

Advancing to step 9:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 22304.769
If we subtract 117 from 120, we 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.

Going ahead to step 10:
13 goes into 30 2 times with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 22304.7692
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.

Moving on to step 11:
40 divided by 13 is 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 22304.76923
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.

Step 12:
The number 13 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 22304.76923
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.

Moving on to step 13:
100 divided by 13 is 7 with a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 22304.7692307
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.

On to step 14:
When dividing 90 by 13, we get 6 with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 22304.76923076
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.

After the division, we end up with 22304.76923076 and a remainder of 1.2e-08.