15738 ÷ 42 
The aim is to understand the frequency of 42 in 15738.

On to step 1:
1 divided by 42 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 42

Moving on to step 2:
When dividing 15 by 42, we get 0 with a remainder of 15.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 15, we get 15.
Grab the next digit (7) from the dividend, add it to 15, then carry on: 157 / 42

On to step 3:
42 can be fit into 157 3 times, resulting in a remainder of 31.
Write down 3 as next digit of the result. 
Result so far: 3.0
If we subtract 126 from 157, we get 31.
Fetch the next digit (3) from the dividend, attach it to 31 and continue: 313 / 42

On to step 4:
The number 42 fits into 313 7 times, leaving a remainder of 19.
Put 7 as the next digit of the answer. 
Result so far: 37.0
Subtract 294 from 313 to get 19.
Append the next digit (8) from the dividend to 19 and continue with: 198 / 42

Going ahead to step 5:
42 can be fit into 198 4 times, resulting in a remainder of 30.
Use 4 as the next digit of our solution. 
Result so far: 374.0
The remainder is 30 after subtracting 168 from 198.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 6:
When dividing 300 by 42, we get 7 with a remainder of 6.
Write down 7 as next digit of the result. 
Result so far: 374.7
Deduct 294 from 300 and we're left with 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 7:
When dividing 60 by 42, we get 1 with a remainder of 18.
Use 1 as the next digit of our solution. 
Result so far: 374.71
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.

Step 8:
The number 42 fits into 180 4 times, leaving a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 374.714
If we subtract 168 from 180, we 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.

On to step 9:
When dividing 120 by 42, we get 2 with a remainder of 36.
Use 2 as the next digit of our solution. 
Result so far: 374.7142
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.

Step 10:
360 divided by 42 is 8 with a remainder of 24.
Write down 8 as next digit of the result. 
Result so far: 374.71428
The remainder is 24 after subtracting 336 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 11:
240 divided by 42 is 5 with a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 374.714285
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 12:
The number 42 fits into 300 7 times, leaving a remainder of 6.
Put 7 as the next digit of the answer. 
Result so far: 374.7142857
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.

Let's proceed to step 13:
The number 42 fits into 60 1 times, leaving a remainder of 18.
The next digit of our result is 1. 
Result so far: 374.71428571
If we take 42 away from 60, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Our division results in 374.71428571 with a remaining 1.8e-08.