We're dividing 309538 by 42 
The aim is to understand the frequency of 42 in 309538.

Step 1:
42 goes into 3 0 times with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 42

Let's proceed to step 2:
When dividing 30 by 42, we get 0 with a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 30, we get 30.
Append the next digit (9) from the dividend to 30 and continue with: 309 / 42

Step 3:
The number 42 fits into 309 7 times, leaving a remainder of 15.
Put 7 as the next digit of the answer. 
Result so far: 7.0
If we subtract 294 from 309, we get 15.
Take the next digit (5) from the dividend and append it to 15, then repeat: 155 / 42

Step 4:
The number 42 fits into 155 3 times, leaving a remainder of 29.
Write down 3 as next digit of the result. 
Result so far: 73.0
The remainder is 29 after subtracting 126 from 155.
Fetch the next digit (3) from the dividend, attach it to 29 and continue: 293 / 42

Going ahead to step 5:
When dividing 293 by 42, we get 6 with a remainder of 41.
Use 6 as the next digit of our solution. 
Result so far: 736.0
If we subtract 252 from 293, we get 41.
Include the next digit (8) from the dividend after 41, then repeat: 418 / 42

Moving on to step 6:
When dividing 418 by 42, we get 9 with a remainder of 40.
The number 9 becomes the next digit in our result. 
Result so far: 7369.0
If we take 378 away from 418, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 7:
If we divide 400 by 42, we get 9 and a remainder of 22.
Record the quotient 9 as the next digit in the result. 
Result so far: 7369.9
If we subtract 378 from 400, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 8:
42 goes into 220 5 times with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 7369.95
Subtract 210 from 220 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
42 goes into 100 2 times with a remainder of 16.
The next digit of our result is 2. 
Result so far: 7369.952
If we subtract 84 from 100, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 10:
If we divide 160 by 42, we get 3 and a remainder of 34.
Write down 3 as next digit of the result. 
Result so far: 7369.9523
Subtracting 126 from 160 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 11:
42 can be fit into 340 8 times, resulting in a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 7369.95238
The remainder is 4 after subtracting 336 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 12:
42 goes into 40 0 times with a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 7369.95238
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 13:
42 can be fit into 400 9 times, resulting in a remainder of 22.
Put 9 as the next digit of the answer. 
Result so far: 7369.9523809
Subtracting 378 from 400 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 14:
The number 42 fits into 220 5 times, leaving a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 7369.95238095
Deduct 210 from 220 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The final outcome is 7369.95238095, with a leftover of 1e-08.