102414 divided by 42 
The aim is to understand the frequency of 42 in 102414.

Step 1:
If we divide 1 by 42, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 42

Step 2:
42 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (2) from the dividend, attach it to 10 and continue: 102 / 42

Moving on to step 3:
42 goes into 102 2 times with a remainder of 18.
The next digit of our result is 2. 
Result so far: 2.0
If we take 84 away from 102, we end up with 18.
Grab the next digit (4) from the dividend, add it to 18, then carry on: 184 / 42

Going ahead to step 4:
42 goes into 184 4 times with a remainder of 16.
The number 4 becomes the next digit in our result. 
Result so far: 24.0
Subtract 168 from 184 to get 16.
Bring next digit (1) of the dividend behind the 16 and repeat the process: 161 / 42

Advancing to step 5:
When dividing 161 by 42, we get 3 with a remainder of 35.
Put 3 as the next digit of the answer. 
Result so far: 243.0
Subtract 126 from 161 to get 35.
Append the next digit (4) from the dividend to 35 and continue with: 354 / 42

Advancing to step 6:
354 divided by 42 is 8 with a remainder of 18.
Record the quotient 8 as the next digit in the result. 
Result so far: 2438.0
The remainder is 18 after subtracting 336 from 354.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 7:
If we divide 180 by 42, we get 4 and a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 2438.4
If we take 168 away from 180, we end up 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 8:
If we divide 120 by 42, we get 2 and a remainder of 36.
Write down 2 as next digit of the result. 
Result so far: 2438.42
Subtract 84 from 120 to get 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:
The number 42 fits into 360 8 times, leaving a remainder of 24.
Put 8 as the next digit of the answer. 
Result so far: 2438.428
Subtracting 336 from 360 leaves us 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.

Let's proceed 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: 2438.4285
Subtracting 210 from 240 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 11:
300 divided by 42 is 7 with a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 2438.42857
Subtract 294 from 300 to 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.

Step 12:
42 can be fit into 60 1 times, resulting in a remainder of 18.
The number 1 becomes the next digit in our result. 
Result so far: 2438.428571
The remainder is 18 after subtracting 42 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 13:
If we divide 180 by 42, we get 4 and a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 2438.4285714
Subtract 168 from 180 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.

Let's proceed to step 14:
42 goes into 120 2 times with a remainder of 36.
Record the quotient 2 as the next digit in the result. 
Result so far: 2438.42857142
Subtracting 84 from 120 leaves us 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 2438.42857142, and the remainder is 3.6e-08.