We're dividing 175838 by 75 
We're looking to find how many times 75 goes into 175838.

Moving on to step 1:
If we divide 1 by 75, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 75

Step 2:
The number 75 fits into 17 0 times, leaving a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 17 after subtracting 0 from 17.
Bring next digit (5) of the dividend behind the 17 and repeat the process: 175 / 75

Advancing to step 3:
75 can be fit into 175 2 times, resulting in a remainder of 25.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we take 150 away from 175, we end up with 25.
Include the next digit (8) from the dividend after 25, then repeat: 258 / 75

Step 4:
258 divided by 75 is 3 with a remainder of 33.
The number 3 becomes the next digit in our result. 
Result so far: 23.0
If we take 225 away from 258, we end up with 33.
Include the next digit (3) from the dividend after 33, then repeat: 333 / 75

Let's proceed to step 5:
75 goes into 333 4 times with a remainder of 33.
Write down 4 as next digit of the result. 
Result so far: 234.0
If we subtract 300 from 333, we get 33.
Append the next digit (8) from the dividend to 33 and continue with: 338 / 75

Moving on to step 6:
The number 75 fits into 338 4 times, leaving a remainder of 38.
Record the quotient 4 as the next digit in the result. 
Result so far: 2344.0
Deduct 300 from 338 and we're left 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.

Moving on to step 7:
If we divide 380 by 75, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 2344.5
If we subtract 375 from 380, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
50 divided by 75 is 0 with a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 2344.5
If we take 0 away from 50, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 9:
75 goes into 500 6 times with a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 2344.506
Subtracting 450 from 500 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 10:
The number 75 fits into 500 6 times, leaving a remainder of 50.
The next digit of our result is 6. 
Result so far: 2344.5066
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final result is 2344.5066 with a remainder of 0.0005.