We're dividing 589629 by 13 
The aim is to understand the frequency of 13 in 589629.

Advancing to step 1:
The number 13 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 13

Step 2:
The number 13 fits into 58 4 times, leaving a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 4.0
The remainder is 6 after subtracting 52 from 58.
Include the next digit (9) from the dividend after 6, then repeat: 69 / 13

Moving on to step 3:
If we divide 69 by 13, we get 5 and a remainder of 4.
Use 5 as the next digit of our solution. 
Result so far: 45.0
The remainder is 4 after subtracting 65 from 69.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 13

Let's proceed to step 4:
13 goes into 46 3 times with a remainder of 7.
The next digit of our result is 3. 
Result so far: 453.0
If we take 39 away from 46, we end up with 7.
Include the next digit (2) from the dividend after 7, then repeat: 72 / 13

Moving on to step 5:
The number 13 fits into 72 5 times, leaving a remainder of 7.
The number 5 becomes the next digit in our result. 
Result so far: 4535.0
The remainder is 7 after subtracting 65 from 72.
Include the next digit (9) from the dividend after 7, then repeat: 79 / 13

Going ahead to step 6:
13 can be fit into 79 6 times, resulting in a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 45356.0
The remainder is 1 after subtracting 78 from 79.
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:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 45356.0
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.

Moving on to step 8:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 45356.07
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 9:
13 can be fit into 90 6 times, resulting in a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 45356.076
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.

Advancing to step 10:
When dividing 120 by 13, we get 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 45356.0769
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.

Step 11:
30 divided by 13 is 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 45356.07692
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.

Advancing to step 12:
40 divided by 13 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 45356.076923
The remainder is 1 after subtracting 39 from 40.
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 13:
When dividing 10 by 13, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 45356.076923
Deduct 0 from 10 and we're left 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 14:
If we divide 100 by 13, we get 7 and a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 45356.07692307
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.

The final result is 45356.07692307 with a remainder of 9e-09.