828397 divided by 78 
The aim is to understand the frequency of 78 in 828397.

Going ahead to step 1:
If we divide 8 by 78, we get 0 and a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Include the next digit (2) from the dividend after 8, then repeat: 82 / 78

Moving on to step 2:
82 divided by 78 is 1 with a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
The remainder is 4 after subtracting 78 from 82.
Include the next digit (8) from the dividend after 4, then repeat: 48 / 78

Step 3:
78 goes into 48 0 times with a remainder of 48.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we subtract 0 from 48, we get 48.
Grab the next digit (3) from the dividend, add it to 48, then carry on: 483 / 78

Going ahead to step 4:
78 goes into 483 6 times with a remainder of 15.
The number 6 becomes the next digit in our result. 
Result so far: 106.0
Deduct 468 from 483 and we're left with 15.
Fetch the next digit (9) from the dividend, attach it to 15 and continue: 159 / 78

Let's proceed to step 5:
The number 78 fits into 159 2 times, leaving a remainder of 3.
Use 2 as the next digit of our solution. 
Result so far: 1062.0
Subtract 156 from 159 to get 3.
Include the next digit (7) from the dividend after 3, then repeat: 37 / 78

Step 6:
78 goes into 37 0 times with a remainder of 37.
The next digit of our result is 0. 
Result so far: 10620.0
Deduct 0 from 37 and we're left with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

On to step 7:
370 divided by 78 is 4 with a remainder of 58.
Write down 4 as next digit of the result. 
Result so far: 10620.4
Subtracting 312 from 370 leaves us with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Advancing to step 8:
580 divided by 78 is 7 with a remainder of 34.
Use 7 as the next digit of our solution. 
Result so far: 10620.47
If we subtract 546 from 580, we get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 9:
340 divided by 78 is 4 with a remainder of 28.
The number 4 becomes the next digit in our result. 
Result so far: 10620.474
If we subtract 312 from 340, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 10:
78 goes into 280 3 times with a remainder of 46.
Record the quotient 3 as the next digit in the result. 
Result so far: 10620.4743
If we take 234 away from 280, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 11:
78 can be fit into 460 5 times, resulting in a remainder of 70.
Write down 5 as next digit of the result. 
Result so far: 10620.47435
If we subtract 390 from 460, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Advancing to step 12:
78 can be fit into 700 8 times, resulting in a remainder of 76.
Put 8 as the next digit of the answer. 
Result so far: 10620.474358
If we take 624 away from 700, we end up with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Step 13:
760 divided by 78 is 9 with a remainder of 58.
Put 9 as the next digit of the answer. 
Result so far: 10620.4743589
If we take 702 away from 760, we end up with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

On to step 14:
If we divide 580 by 78, we get 7 and a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 10620.47435897
Deduct 546 from 580 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

The final result is 10620.47435897 with a remainder of 3.4e-08.