509906 ÷ 75 
We're looking to find how many times 75 goes into 509906.

Moving on to step 1:
75 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 75

Advancing to step 2:
75 goes into 50 0 times with a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 50, we end up with 50.
Take the next digit (9) from the dividend and append it to 50, then repeat: 509 / 75

Moving on to step 3:
If we divide 509 by 75, we get 6 and a remainder of 59.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 59 after subtracting 450 from 509.
Take the next digit (9) from the dividend and append it to 59, then repeat: 599 / 75

Advancing to step 4:
75 can be fit into 599 7 times, resulting in a remainder of 74.
Put 7 as the next digit of the answer. 
Result so far: 67.0
Subtract 525 from 599 to get 74.
Grab the next digit (0) from the dividend, add it to 74, then carry on: 740 / 75

Going ahead to step 5:
If we divide 740 by 75, we get 9 and a remainder of 65.
Write down 9 as next digit of the result. 
Result so far: 679.0
The remainder is 65 after subtracting 675 from 740.
Grab the next digit (6) from the dividend, add it to 65, then carry on: 656 / 75

Moving on to step 6:
If we divide 656 by 75, we get 8 and a remainder of 56.
The next digit of our result is 8. 
Result so far: 6798.0
If we subtract 600 from 656, we get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 7:
75 can be fit into 560 7 times, resulting in a remainder of 35.
The next digit of our result is 7. 
Result so far: 6798.7
Subtract 525 from 560 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Going ahead to step 8:
If we divide 350 by 75, we get 4 and a remainder of 50.
Record the quotient 4 as the next digit in the result. 
Result so far: 6798.74
If we subtract 300 from 350, 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.

On to step 9:
500 divided by 75 is 6 with a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 6798.746
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.

Step 10:
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: 6798.7466
If we take 450 away from 500, 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.

The quotient of the division is 6798.7466, and the remainder is 0.0005.