421841 divided by 42 
The aim is to understand the frequency of 42 in 421841.

Let's proceed to step 1:
4 divided by 42 is 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 42

On to step 2:
42 divided by 42 is 1 with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 42 away from 42, we end up with 0.
Append the next digit (1) from the dividend to 0 and continue with: 1 / 42

Advancing to step 3:
If we divide 1 by 42, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we take 0 away from 1, we end up with 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 42

Step 4:
If we divide 18 by 42, we get 0 and a remainder of 18.
Put 0 as the next digit of the answer. 
Result so far: 100.0
Deduct 0 from 18 and we're left with 18.
Fetch the next digit (4) from the dividend, attach it to 18 and continue: 184 / 42

Advancing to step 5:
42 can be fit into 184 4 times, resulting in a remainder of 16.
Put 4 as the next digit of the answer. 
Result so far: 1004.0
Subtracting 168 from 184 leaves us with 16.
Grab the next digit (1) from the dividend, add it to 16, then carry on: 161 / 42

Going ahead to step 6:
42 goes into 161 3 times with a remainder of 35.
Use 3 as the next digit of our solution. 
Result so far: 10043.0
The remainder is 35 after subtracting 126 from 161.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 7:
42 goes into 350 8 times with a remainder of 14.
Put 8 as the next digit of the answer. 
Result so far: 10043.8
Subtract 336 from 350 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 8:
42 can be fit into 140 3 times, resulting in a remainder of 14.
The next digit of our result is 3. 
Result so far: 10043.83
Deduct 126 from 140 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 9:
The number 42 fits into 140 3 times, leaving a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 10043.833
Subtracting 126 from 140 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

In conclusion, the division gives 10043.833 with a balance of 0.0014.