687724 ÷ 13 
The aim is to understand the frequency of 13 in 687724.

Moving on to step 1:
If we divide 6 by 13, we get 0 and a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 13

On to step 2:
The number 13 fits into 68 5 times, leaving a remainder of 3.
The next digit of our result is 5. 
Result so far: 5.0
Subtract 65 from 68 to get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 13

Going ahead to step 3:
37 divided by 13 is 2 with a remainder of 11.
Write down 2 as next digit of the result. 
Result so far: 52.0
The remainder is 11 after subtracting 26 from 37.
Include the next digit (7) from the dividend after 11, then repeat: 117 / 13

On to step 4:
13 goes into 117 9 times with a remainder of 0.
Put 9 as the next digit of the answer. 
Result so far: 529.0
Deduct 117 from 117 and we're left with 0.
Take the next digit (2) from the dividend and append it to 0, then repeat: 2 / 13

Moving on to step 5:
13 can be fit into 2 0 times, resulting in a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 5290.0
Subtracting 0 from 2 leaves us with 2.
Grab the next digit (4) from the dividend, add it to 2, then carry on: 24 / 13

Going ahead to step 6:
When dividing 24 by 13, we get 1 with a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 52901.0
Deduct 13 from 24 and we're left 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.

Step 7:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 52901.8
Subtracting 104 from 110 leaves us 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.

Step 8:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 52901.84
Deduct 52 from 60 and we're left 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.

Let's proceed to step 9:
13 goes into 80 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 52901.846
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.

Let's proceed to step 10:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 52901.8461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 11:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 52901.84615
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.

On to step 12:
13 can be fit into 50 3 times, resulting in a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 52901.846153
If we subtract 39 from 50, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 13:
110 divided by 13 is 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 52901.8461538
Subtracting 104 from 110 leaves us 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.

Step 14:
When dividing 60 by 13, we get 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 52901.84615384
Deduct 52 from 60 and we're left 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.

In conclusion, the division gives 52901.84615384 with a balance of 8e-09.