We're dividing 75205914 by 553 
Our goal is to divide 75205914 by 553.

Advancing to step 1:
When dividing 7 by 553, we get 0 with a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 553

On to step 2:
75 divided by 553 is 0 with a remainder of 75.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 75 after subtracting 0 from 75.
Bring next digit (2) of the dividend behind the 75 and repeat the process: 752 / 553

Advancing to step 3:
If we divide 752 by 553, we get 1 and a remainder of 199.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 199 after subtracting 553 from 752.
Take the next digit (0) from the dividend and append it to 199, then repeat: 1990 / 553

Moving on to step 4:
The number 553 fits into 1990 3 times, leaving a remainder of 331.
The number 3 becomes the next digit in our result. 
Result so far: 13.0
Deduct 1659 from 1990 and we're left with 331.
Include the next digit (5) from the dividend after 331, then repeat: 3315 / 553

Moving on to step 5:
553 goes into 3315 5 times with a remainder of 550.
The next digit of our result is 5. 
Result so far: 135.0
The remainder is 550 after subtracting 2765 from 3315.
Take the next digit (9) from the dividend and append it to 550, then repeat: 5509 / 553

Moving on to step 6:
553 can be fit into 5509 9 times, resulting in a remainder of 532.
The next digit of our result is 9. 
Result so far: 1359.0
Subtract 4977 from 5509 to get 532.
Bring next digit (1) of the dividend behind the 532 and repeat the process: 5321 / 553

Step 7:
553 can be fit into 5321 9 times, resulting in a remainder of 344.
Use 9 as the next digit of our solution. 
Result so far: 13599.0
Subtracting 4977 from 5321 leaves us with 344.
Bring next digit (4) of the dividend behind the 344 and repeat the process: 3444 / 553

Step 8:
When dividing 3444 by 553, we get 6 with a remainder of 126.
The next digit of our result is 6. 
Result so far: 135996.0
If we take 3318 away from 3444, we end up with 126.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1260, and continue the process.

Advancing to step 9:
When dividing 1260 by 553, we get 2 with a remainder of 154.
Use 2 as the next digit of our solution. 
Result so far: 135996.2
Subtract 1106 from 1260 to get 154.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1540, and continue the process.

Let's proceed to step 10:
553 goes into 1540 2 times with a remainder of 434.
Use 2 as the next digit of our solution. 
Result so far: 135996.22
If we take 1106 away from 1540, we end up with 434.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4340, and continue the process.

The quotient of the division is 135996.22, and the remainder is 0.434.