We're dividing 105722 by 78 
The aim is to understand the frequency of 78 in 105722.

On to step 1:
When dividing 1 by 78, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 78

Step 2:
When dividing 10 by 78, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 78

Advancing to step 3:
When dividing 105 by 78, we get 1 with a remainder of 27.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 78 from 105, we get 27.
Grab the next digit (7) from the dividend, add it to 27, then carry on: 277 / 78

Let's proceed to step 4:
If we divide 277 by 78, we get 3 and a remainder of 43.
Put 3 as the next digit of the answer. 
Result so far: 13.0
The remainder is 43 after subtracting 234 from 277.
Grab the next digit (2) from the dividend, add it to 43, then carry on: 432 / 78

Let's proceed to step 5:
78 goes into 432 5 times with a remainder of 42.
Write down 5 as next digit of the result. 
Result so far: 135.0
The remainder is 42 after subtracting 390 from 432.
Grab the next digit (2) from the dividend, add it to 42, then carry on: 422 / 78

Step 6:
78 goes into 422 5 times with a remainder of 32.
Write down 5 as next digit of the result. 
Result so far: 1355.0
The remainder is 32 after subtracting 390 from 422.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 7:
When dividing 320 by 78, we get 4 with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 1355.4
The remainder is 8 after subtracting 312 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 8:
When dividing 80 by 78, we get 1 with a remainder of 2.
The next digit of our result is 1. 
Result so far: 1355.41
If we take 78 away from 80, we end up with 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 9:
78 goes into 20 0 times with a remainder of 20.
The next digit of our result is 0. 
Result so far: 1355.41
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 10:
The number 78 fits into 200 2 times, leaving a remainder of 44.
The number 2 becomes the next digit in our result. 
Result so far: 1355.4102
The remainder is 44 after subtracting 156 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 11:
440 divided by 78 is 5 with a remainder of 50.
The next digit of our result is 5. 
Result so far: 1355.41025
The remainder is 50 after subtracting 390 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 12:
The number 78 fits into 500 6 times, leaving a remainder of 32.
Record the quotient 6 as the next digit in the result. 
Result so far: 1355.410256
Deduct 468 from 500 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Going ahead to step 13:
78 can be fit into 320 4 times, resulting in a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 1355.4102564
The remainder is 8 after subtracting 312 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 14:
The number 78 fits into 80 1 times, leaving a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 1355.41025641
Deduct 78 from 80 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 1355.41025641 and a remainder of 2e-09.