697687 divided by 78 
The aim is to understand the frequency of 78 in 697687.

Going ahead to step 1:
If we divide 6 by 78, we get 0 and a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (9) from the dividend and append it to 6, then repeat: 69 / 78

Step 2:
69 divided by 78 is 0 with a remainder of 69.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 69 after subtracting 0 from 69.
Append the next digit (7) from the dividend to 69 and continue with: 697 / 78

On to step 3:
78 can be fit into 697 8 times, resulting in a remainder of 73.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Subtract 624 from 697 to get 73.
Fetch the next digit (6) from the dividend, attach it to 73 and continue: 736 / 78

Step 4:
78 can be fit into 736 9 times, resulting in a remainder of 34.
Record the quotient 9 as the next digit in the result. 
Result so far: 89.0
Subtracting 702 from 736 leaves us with 34.
Grab the next digit (8) from the dividend, add it to 34, then carry on: 348 / 78

Moving on to step 5:
When dividing 348 by 78, we get 4 with a remainder of 36.
The next digit of our result is 4. 
Result so far: 894.0
Subtract 312 from 348 to get 36.
Grab the next digit (7) from the dividend, add it to 36, then carry on: 367 / 78

Going ahead to step 6:
78 can be fit into 367 4 times, resulting in a remainder of 55.
Use 4 as the next digit of our solution. 
Result so far: 8944.0
Deduct 312 from 367 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 7:
550 divided by 78 is 7 with a remainder of 4.
Record the quotient 7 as the next digit in the result. 
Result so far: 8944.7
If we take 546 away from 550, we end up with 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 8:
The number 78 fits into 40 0 times, leaving a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 8944.7
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 9:
78 can be fit into 400 5 times, resulting in a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 8944.705
The remainder is 10 after subtracting 390 from 400.
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 10:
The number 78 fits into 100 1 times, leaving a remainder of 22.
Record the quotient 1 as the next digit in the result. 
Result so far: 8944.7051
If we take 78 away from 100, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 11:
78 can be fit into 220 2 times, resulting in a remainder of 64.
Write down 2 as next digit of the result. 
Result so far: 8944.70512
If we take 156 away from 220, we end up with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Moving on to step 12:
640 divided by 78 is 8 with a remainder of 16.
The next digit of our result is 8. 
Result so far: 8944.705128
If we take 624 away from 640, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 13:
The number 78 fits into 160 2 times, leaving a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 8944.7051282
Subtracting 156 from 160 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 14:
78 goes into 40 0 times with a remainder of 40.
The next digit of our result is 0. 
Result so far: 8944.7051282
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

In conclusion, the division gives 8944.7051282 with a balance of 4e-08.