We divide 513875 by 42
We want to figure out the number of times 513875 can be divided by 42.

Going ahead to step 1:
5 divided by 42 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 42

Step 2:
42 goes into 51 1 times with a remainder of 9.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 42 from 51 leaves us with 9.
Include the next digit (3) from the dividend after 9, then repeat: 93 / 42

Going ahead to step 3:
The number 42 fits into 93 2 times, leaving a remainder of 9.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
If we subtract 84 from 93, we get 9.
Include the next digit (8) from the dividend after 9, then repeat: 98 / 42

Moving on to step 4:
42 goes into 98 2 times with a remainder of 14.
Record the quotient 2 as the next digit in the result. 
Result so far: 122.0
Subtract 84 from 98 to get 14.
Append the next digit (7) from the dividend to 14 and continue with: 147 / 42

Let's proceed to step 5:
42 goes into 147 3 times with a remainder of 21.
Write down 3 as next digit of the result. 
Result so far: 1223.0
Subtracting 126 from 147 leaves us with 21.
Append the next digit (5) from the dividend to 21 and continue with: 215 / 42

Step 6:
215 divided by 42 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 12235.0
Deduct 210 from 215 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 7:
42 goes into 50 1 times with a remainder of 8.
The next digit of our result is 1. 
Result so far: 12235.1
Subtract 42 from 50 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 8:
42 goes into 80 1 times with a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 12235.11
If we take 42 away from 80, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The quotient of the division is 12235.11, and the remainder is 0.038.