Let's divide 217641 by 42
The aim is to understand the frequency of 42 in 217641.

Advancing to step 1:
When dividing 2 by 42, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 42

Moving on to step 2:
42 can be fit into 21 0 times, resulting in a remainder of 21.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 21 leaves us with 21.
Grab the next digit (7) from the dividend, add it to 21, then carry on: 217 / 42

Going ahead to step 3:
If we divide 217 by 42, we get 5 and a remainder of 7.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 210 from 217, we get 7.
Include the next digit (6) from the dividend after 7, then repeat: 76 / 42

Going ahead to step 4:
42 goes into 76 1 times with a remainder of 34.
The next digit of our result is 1. 
Result so far: 51.0
Subtracting 42 from 76 leaves us with 34.
Append the next digit (4) from the dividend to 34 and continue with: 344 / 42

Going ahead to step 5:
42 goes into 344 8 times with a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 518.0
The remainder is 8 after subtracting 336 from 344.
Grab the next digit (1) from the dividend, add it to 8, then carry on: 81 / 42

On to step 6:
42 goes into 81 1 times with a remainder of 39.
Put 1 as the next digit of the answer. 
Result so far: 5181.0
If we take 42 away from 81, we end up with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Going ahead to step 7:
390 divided by 42 is 9 with a remainder of 12.
Write down 9 as next digit of the result. 
Result so far: 5181.9
Subtract 378 from 390 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 8:
120 divided by 42 is 2 with a remainder of 36.
The next digit of our result is 2. 
Result so far: 5181.92
Deduct 84 from 120 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 9:
42 goes into 360 8 times with a remainder of 24.
Put 8 as the next digit of the answer. 
Result so far: 5181.928
If we take 336 away from 360, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 10:
42 goes into 240 5 times with a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 5181.9285
Subtract 210 from 240 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 11:
42 goes into 300 7 times with a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 5181.92857
If we subtract 294 from 300, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 12:
If we divide 60 by 42, we get 1 and a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 5181.928571
If we subtract 42 from 60, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 13:
If we divide 180 by 42, we get 4 and a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 5181.9285714
Deduct 168 from 180 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 14:
120 divided by 42 is 2 with a remainder of 36.
Use 2 as the next digit of our solution. 
Result so far: 5181.92857142
If we take 84 away from 120, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

The quotient of the division is 5181.92857142, and the remainder is 3.6e-08.