503533 ÷ 42 
The aim is to understand the frequency of 42 in 503533.

On to step 1:
42 goes into 5 0 times with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 42

Moving on to step 2:
42 can be fit into 50 1 times, resulting in a remainder of 8.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 42 away from 50, we end up with 8.
Grab the next digit (3) from the dividend, add it to 8, then carry on: 83 / 42

Step 3:
The number 42 fits into 83 1 times, leaving a remainder of 41.
Use 1 as the next digit of our solution. 
Result so far: 11.0
The remainder is 41 after subtracting 42 from 83.
Bring next digit (5) of the dividend behind the 41 and repeat the process: 415 / 42

Advancing to step 4:
The number 42 fits into 415 9 times, leaving a remainder of 37.
Use 9 as the next digit of our solution. 
Result so far: 119.0
Deduct 378 from 415 and we're left with 37.
Fetch the next digit (3) from the dividend, attach it to 37 and continue: 373 / 42

On to step 5:
The number 42 fits into 373 8 times, leaving a remainder of 37.
The next digit of our result is 8. 
Result so far: 1198.0
Subtract 336 from 373 to get 37.
Grab the next digit (3) from the dividend, add it to 37, then carry on: 373 / 42

Advancing to step 6:
If we divide 373 by 42, we get 8 and a remainder of 37.
Put 8 as the next digit of the answer. 
Result so far: 11988.0
Subtract 336 from 373 to get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Moving on to step 7:
370 divided by 42 is 8 with a remainder of 34.
The next digit of our result is 8. 
Result so far: 11988.8
Subtract 336 from 370 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 8:
42 can be fit into 340 8 times, resulting in a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 11988.88
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.

The quotient of the division is 11988.88, and the remainder is 0.004.