561667 ÷ 13 
The aim is to understand the frequency of 13 in 561667.

Step 1:
When dividing 5 by 13, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 13

Going ahead to step 2:
If we divide 56 by 13, we get 4 and a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 4.0
Deduct 52 from 56 and we're left with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 13

Step 3:
When dividing 41 by 13, we get 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 43.0
Deduct 39 from 41 and we're left with 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 13

Moving on to step 4:
13 can be fit into 26 2 times, resulting in a remainder of 0.
Record the quotient 2 as the next digit in the result. 
Result so far: 432.0
Deduct 26 from 26 and we're left with 0.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 13

Advancing to step 5:
13 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 4320.0
Subtract 0 from 6 to get 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 13

On to step 6:
13 can be fit into 67 5 times, resulting in a remainder of 2.
Record the quotient 5 as the next digit in the result. 
Result so far: 43205.0
If we take 65 away from 67, we end up 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 7:
If we divide 20 by 13, we get 1 and a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 43205.1
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.

Moving on to step 8:
13 goes into 70 5 times with a remainder of 5.
The next digit of our result is 5. 
Result so far: 43205.15
If we subtract 65 from 70, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 9:
The number 13 fits into 50 3 times, leaving a remainder of 11.
The next digit of our result is 3. 
Result so far: 43205.153
Subtracting 39 from 50 leaves us 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.

Going ahead to step 10:
110 divided by 13 is 8 with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 43205.1538
The remainder is 6 after subtracting 104 from 110.
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 11:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 43205.15384
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 12:
80 divided by 13 is 6 with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 43205.153846
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 13:
If we divide 20 by 13, we get 1 and a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 43205.1538461
Deduct 13 from 20 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 14:
70 divided by 13 is 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 43205.15384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final result is 43205.15384615 with a remainder of 5e-09.