401971 ÷ 13 
The aim is to understand the frequency of 13 in 401971.

On to step 1:
When dividing 4 by 13, we get 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 13

Moving on to step 2:
13 can be fit into 40 3 times, resulting in a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 3.0
Subtracting 39 from 40 leaves us with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 13

Let's proceed to step 3:
11 divided by 13 is 0 with a remainder of 11.
The next digit of our result is 0. 
Result so far: 30.0
Subtract 0 from 11 to get 11.
Fetch the next digit (9) from the dividend, attach it to 11 and continue: 119 / 13

Moving on to step 4:
119 divided by 13 is 9 with a remainder of 2.
Use 9 as the next digit of our solution. 
Result so far: 309.0
The remainder is 2 after subtracting 117 from 119.
Fetch the next digit (7) from the dividend, attach it to 2 and continue: 27 / 13

Going ahead to step 5:
13 can be fit into 27 2 times, resulting in a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 3092.0
Deduct 26 from 27 and we're left with 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 13

Step 6:
13 goes into 11 0 times with a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 30920.0
Subtract 0 from 11 to 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.

Advancing to step 7:
13 goes into 110 8 times with a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 30920.8
If we take 104 away from 110, we end up 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.

Advancing to step 8:
13 can be fit into 60 4 times, resulting in a remainder of 8.
The next digit of our result is 4. 
Result so far: 30920.84
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.

On to step 9:
80 divided by 13 is 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 30920.846
Subtract 78 from 80 to 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.

Going ahead to step 10:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 30920.8461
If we take 13 away from 20, we end up 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.

Step 11:
13 goes into 70 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 30920.84615
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.

Let's proceed to step 12:
If we divide 50 by 13, we get 3 and a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 30920.846153
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:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 30920.8461538
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:
The number 13 fits into 60 4 times, leaving a remainder of 8.
The next digit of our result is 4. 
Result so far: 30920.84615384
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.

The final result is 30920.84615384 with a remainder of 8e-09.