406977 divided by 13 
The aim is to understand the frequency of 13 in 406977.

Step 1:
The number 13 fits into 4 0 times, leaving a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 13

Advancing to step 2:
The number 13 fits into 40 3 times, leaving 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.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 13

Going ahead to step 3:
If we divide 16 by 13, we get 1 and a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 31.0
Subtract 13 from 16 to get 3.
Append the next digit (9) from the dividend to 3 and continue with: 39 / 13

Moving on to step 4:
When dividing 39 by 13, we get 3 with a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 313.0
Subtract 39 from 39 to get 0.
Grab the next digit (7) from the dividend, add it to 0, then carry on: 7 / 13

Let's proceed to step 5:
When dividing 7 by 13, we get 0 with a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 3130.0
Subtracting 0 from 7 leaves us with 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 13

Going ahead to step 6:
77 divided by 13 is 5 with a remainder of 12.
Record the quotient 5 as the next digit in the result. 
Result so far: 31305.0
If we subtract 65 from 77, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 7:
When dividing 120 by 13, we get 9 with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 31305.9
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 8:
13 goes into 30 2 times with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 31305.92
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.

Advancing to step 9:
When dividing 40 by 13, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 31305.923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 10:
10 divided by 13 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 31305.923
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 11:
The number 13 fits into 100 7 times, leaving a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 31305.92307
Subtracting 91 from 100 leaves us 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.

On to step 12:
When dividing 90 by 13, we get 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 31305.923076
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 13:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 31305.9230769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 14:
If we divide 30 by 13, we get 2 and a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 31305.92307692
Subtract 26 from 30 to 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.

The final outcome is 31305.92307692, with a leftover of 4e-09.