532840 ÷ 13 
The aim is to understand the frequency of 13 in 532840.

Step 1:
If we divide 5 by 13, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (3) from the dividend and append it to 5, then repeat: 53 / 13

On to step 2:
If we divide 53 by 13, we get 4 and a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we take 52 away from 53, we end up with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 13

Step 3:
If we divide 12 by 13, we get 0 and a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 40.0
The remainder is 12 after subtracting 0 from 12.
Grab the next digit (8) from the dividend, add it to 12, then carry on: 128 / 13

Advancing to step 4:
When dividing 128 by 13, we get 9 with a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 409.0
If we subtract 117 from 128, we get 11.
Grab the next digit (4) from the dividend, add it to 11, then carry on: 114 / 13

On to step 5:
If we divide 114 by 13, we get 8 and a remainder of 10.
Use 8 as the next digit of our solution. 
Result so far: 4098.0
The remainder is 10 after subtracting 104 from 114.
Fetch the next digit (0) from the dividend, attach it to 10 and continue: 100 / 13

Going ahead to step 6:
13 goes into 100 7 times with a remainder of 9.
The next digit of our result is 7. 
Result so far: 40987.0
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.

Let's proceed to step 7:
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: 40987.6
Deduct 78 from 90 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 8:
The number 13 fits into 120 9 times, leaving a remainder of 3.
The next digit of our result is 9. 
Result so far: 40987.69
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 9:
If we divide 30 by 13, we get 2 and a remainder of 4.
The next digit of our result is 2. 
Result so far: 40987.692
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.

Step 10:
If we divide 40 by 13, we get 3 and a remainder of 1.
The next digit of our result is 3. 
Result so far: 40987.6923
If we take 39 away from 40, we end up 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.

Going ahead to step 11:
If we divide 10 by 13, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 40987.6923
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:
100 divided by 13 is 7 with a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 40987.692307
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.

Step 13:
If we divide 90 by 13, we get 6 and a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 40987.6923076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 14:
If we divide 120 by 13, we get 9 and a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 40987.69230769
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.

After the division, we end up with 40987.69230769 and a remainder of 3e-09.