508534 ÷ 75 
We're looking to find how many times 75 goes into 508534.

Moving on to step 1:
75 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 75

Let's proceed to step 2:
50 divided by 75 is 0 with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Include the next digit (8) from the dividend after 50, then repeat: 508 / 75

On to step 3:
75 goes into 508 6 times with a remainder of 58.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 450 away from 508, we end up with 58.
Grab the next digit (5) from the dividend, add it to 58, then carry on: 585 / 75

Moving on to step 4:
75 can be fit into 585 7 times, resulting in a remainder of 60.
The next digit of our result is 7. 
Result so far: 67.0
The remainder is 60 after subtracting 525 from 585.
Fetch the next digit (3) from the dividend, attach it to 60 and continue: 603 / 75

Let's proceed to step 5:
75 can be fit into 603 8 times, resulting in a remainder of 3.
The next digit of our result is 8. 
Result so far: 678.0
The remainder is 3 after subtracting 600 from 603.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 75

On to step 6:
75 goes into 34 0 times with a remainder of 34.
Write down 0 as next digit of the result. 
Result so far: 6780.0
The remainder is 34 after subtracting 0 from 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 7:
If we divide 340 by 75, we get 4 and a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 6780.4
If we take 300 away from 340, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 8:
400 divided by 75 is 5 with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 6780.45
If we take 375 away from 400, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 9:
When dividing 250 by 75, we get 3 with a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 6780.453
If we take 225 away from 250, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 10:
75 goes into 250 3 times with a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 6780.4533
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The final outcome is 6780.4533, with a leftover of 0.00025.