We look at the division of 34638 by 13 
The aim is to understand the frequency of 13 in 34638.

Step 1:
13 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 13

Step 2:
13 goes into 34 2 times with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 26 away from 34, we end up with 8.
Append the next digit (6) from the dividend to 8 and continue with: 86 / 13

Going ahead to step 3:
13 goes into 86 6 times with a remainder of 8.
Use 6 as the next digit of our solution. 
Result so far: 26.0
Subtract 78 from 86 to get 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 13

Advancing to step 4:
If we divide 83 by 13, we get 6 and a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 266.0
Deduct 78 from 83 and we're left with 5.
Grab the next digit (8) from the dividend, add it to 5, then carry on: 58 / 13

Step 5:
When dividing 58 by 13, we get 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 2664.0
Subtract 52 from 58 to 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.

Advancing to step 6:
If we divide 60 by 13, we get 4 and a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 2664.4
If we take 52 away from 60, we end up 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.

Step 7:
13 goes into 80 6 times with a remainder of 2.
The next digit of our result is 6. 
Result so far: 2664.46
Subtracting 78 from 80 leaves us with 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 8:
When dividing 20 by 13, we get 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 2664.461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 9:
If we divide 70 by 13, we get 5 and a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 2664.4615
Subtracting 65 from 70 leaves us with 5.
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 10:
50 divided by 13 is 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 2664.46153
If we take 39 away from 50, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 11:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 2664.461538
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.

Let's proceed to step 12:
If we divide 60 by 13, we get 4 and a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 2664.4615384
If we take 52 away from 60, we end up 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.

Advancing to step 13:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 2664.46153846
The remainder is 2 after subtracting 78 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

In conclusion, the division gives 2664.46153846 with a balance of 2e-09.