We look at the division of 557387 by 75 
We're looking to find how many times 75 goes into 557387.

Going ahead to step 1:
75 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 75

On to step 2:
If we divide 55 by 75, we get 0 and a remainder of 55.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 55 and we're left with 55.
Include the next digit (7) from the dividend after 55, then repeat: 557 / 75

Advancing to step 3:
If we divide 557 by 75, we get 7 and a remainder of 32.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
If we subtract 525 from 557, we get 32.
Include the next digit (3) from the dividend after 32, then repeat: 323 / 75

Let's proceed to step 4:
When dividing 323 by 75, we get 4 with a remainder of 23.
The next digit of our result is 4. 
Result so far: 74.0
Deduct 300 from 323 and we're left with 23.
Grab the next digit (8) from the dividend, add it to 23, then carry on: 238 / 75

Step 5:
The number 75 fits into 238 3 times, leaving a remainder of 13.
The next digit of our result is 3. 
Result so far: 743.0
Subtracting 225 from 238 leaves us with 13.
Grab the next digit (7) from the dividend, add it to 13, then carry on: 137 / 75

Going ahead to step 6:
75 goes into 137 1 times with a remainder of 62.
Record the quotient 1 as the next digit in the result. 
Result so far: 7431.0
Deduct 75 from 137 and we're left with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 7:
75 can be fit into 620 8 times, resulting in a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 7431.8
The remainder is 20 after subtracting 600 from 620.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
When dividing 200 by 75, we get 2 with a remainder of 50.
Put 2 as the next digit of the answer. 
Result so far: 7431.82
Deduct 150 from 200 and we're left 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:
When dividing 500 by 75, we get 6 with a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 7431.826
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.

Moving on to step 10:
500 divided by 75 is 6 with a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 7431.8266
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.

After the division, we end up with 7431.8266 and a remainder of 0.0005.