778597 ÷ 13 
The aim is to understand the frequency of 13 in 778597.

Moving on to step 1:
13 can be fit into 7 0 times, resulting in a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 13

Step 2:
77 divided by 13 is 5 with a remainder of 12.
The next digit of our result is 5. 
Result so far: 5.0
If we subtract 65 from 77, we get 12.
Take the next digit (8) from the dividend and append it to 12, then repeat: 128 / 13

On to step 3:
The number 13 fits into 128 9 times, leaving a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 59.0
If we subtract 117 from 128, we get 11.
Grab the next digit (5) from the dividend, add it to 11, then carry on: 115 / 13

Going ahead to step 4:
If we divide 115 by 13, we get 8 and a remainder of 11.
The number 8 becomes the next digit in our result. 
Result so far: 598.0
Subtracting 104 from 115 leaves us with 11.
Take the next digit (9) from the dividend and append it to 11, then repeat: 119 / 13

Moving on to step 5:
The number 13 fits into 119 9 times, leaving a remainder of 2.
Record the quotient 9 as the next digit in the result. 
Result so far: 5989.0
Deduct 117 from 119 and we're left with 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 13

Moving on to step 6:
13 can be fit into 27 2 times, resulting in a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 59892.0
Deduct 26 from 27 and we're left 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.

Let's proceed to step 7:
10 divided by 13 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 59892.0
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.

Advancing to step 8:
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: 59892.07
If we take 91 away from 100, we end up 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.

Advancing to step 9:
13 goes into 90 6 times with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 59892.076
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.

On to step 10:
13 goes into 120 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 59892.0769
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 11:
13 goes into 30 2 times with a remainder of 4.
The next digit of our result is 2. 
Result so far: 59892.07692
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.

Moving on to step 12:
The number 13 fits into 40 3 times, leaving a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 59892.076923
Subtracting 39 from 40 leaves us 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.

Advancing to step 13:
10 divided by 13 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 59892.076923
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.

Advancing to step 14:
13 goes into 100 7 times with a remainder of 9.
The next digit of our result is 7. 
Result so far: 59892.07692307
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.

In conclusion, the division gives 59892.07692307 with a balance of 9e-09.