We're dividing 557877 by 42 
The aim is to understand the frequency of 42 in 557877.

Step 1:
If we divide 5 by 42, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 42

Step 2:
The number 42 fits into 55 1 times, leaving a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 42 from 55 to get 13.
Grab the next digit (7) from the dividend, add it to 13, then carry on: 137 / 42

On to step 3:
When dividing 137 by 42, we get 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
If we take 126 away from 137, we end up with 11.
Include the next digit (8) from the dividend after 11, then repeat: 118 / 42

Let's proceed to step 4:
The number 42 fits into 118 2 times, leaving a remainder of 34.
Use 2 as the next digit of our solution. 
Result so far: 132.0
The remainder is 34 after subtracting 84 from 118.
Append the next digit (7) from the dividend to 34 and continue with: 347 / 42

Step 5:
The number 42 fits into 347 8 times, leaving a remainder of 11.
Write down 8 as next digit of the result. 
Result so far: 1328.0
If we subtract 336 from 347, we get 11.
Include the next digit (7) from the dividend after 11, then repeat: 117 / 42

Moving on to step 6:
The number 42 fits into 117 2 times, leaving a remainder of 33.
The next digit of our result is 2. 
Result so far: 13282.0
Subtracting 84 from 117 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 7:
The number 42 fits into 330 7 times, leaving a remainder of 36.
Put 7 as the next digit of the answer. 
Result so far: 13282.7
If we subtract 294 from 330, we 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.

On to step 8:
If we divide 360 by 42, we get 8 and a remainder of 24.
Write down 8 as next digit of the result. 
Result so far: 13282.78
If we subtract 336 from 360, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 9:
When dividing 240 by 42, we get 5 with a remainder of 30.
The next digit of our result is 5. 
Result so far: 13282.785
Deduct 210 from 240 and we're left 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.

Advancing to step 10:
42 goes into 300 7 times with a remainder of 6.
Use 7 as the next digit of our solution. 
Result so far: 13282.7857
If we take 294 away from 300, we end up 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.

Moving on to step 11:
The number 42 fits into 60 1 times, leaving a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 13282.78571
Subtract 42 from 60 to 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.

Moving on to step 12:
180 divided by 42 is 4 with a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 13282.785714
The remainder is 12 after subtracting 168 from 180.
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 13:
120 divided by 42 is 2 with a remainder of 36.
Record the quotient 2 as the next digit in the result. 
Result so far: 13282.7857142
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.

Let's proceed to step 14:
42 can be fit into 360 8 times, resulting in a remainder of 24.
The next digit of our result is 8. 
Result so far: 13282.78571428
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.

The quotient of the division is 13282.78571428, and the remainder is 2.4e-08.