Let's divide 421642 by 78
The aim is to understand the frequency of 78 in 421642.

Going ahead to step 1:
When dividing 4 by 78, we get 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 78

Advancing to step 2:
42 divided by 78 is 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 42 to get 42.
Bring next digit (1) of the dividend behind the 42 and repeat the process: 421 / 78

Step 3:
78 goes into 421 5 times with a remainder of 31.
The next digit of our result is 5. 
Result so far: 5.0
Subtract 390 from 421 to get 31.
Bring next digit (6) of the dividend behind the 31 and repeat the process: 316 / 78

Step 4:
The number 78 fits into 316 4 times, leaving a remainder of 4.
The next digit of our result is 4. 
Result so far: 54.0
Subtracting 312 from 316 leaves us with 4.
Append the next digit (4) from the dividend to 4 and continue with: 44 / 78

On to step 5:
The number 78 fits into 44 0 times, leaving a remainder of 44.
The next digit of our result is 0. 
Result so far: 540.0
Subtract 0 from 44 to get 44.
Fetch the next digit (2) from the dividend, attach it to 44 and continue: 442 / 78

Moving on to step 6:
78 can be fit into 442 5 times, resulting in a remainder of 52.
The number 5 becomes the next digit in our result. 
Result so far: 5405.0
If we take 390 away from 442, we end up with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Advancing to step 7:
78 can be fit into 520 6 times, resulting in a remainder of 52.
Record the quotient 6 as the next digit in the result. 
Result so far: 5405.6
Subtract 468 from 520 to get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 8:
If we divide 520 by 78, we get 6 and a remainder of 52.
Write down 6 as next digit of the result. 
Result so far: 5405.66
Deduct 468 from 520 and we're left with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

The final result is 5405.66 with a remainder of 0.052.