We're dividing 509567 by 30 
Our goal is to divide 509567 by 30.

Going ahead to step 1:
The number 30 fits into 5 0 times, leaving 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.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 30

Advancing to step 2:
50 divided by 30 is 1 with a remainder of 20.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 30 from 50 leaves us with 20.
Grab the next digit (9) from the dividend, add it to 20, then carry on: 209 / 30

On to step 3:
30 can be fit into 209 6 times, resulting in a remainder of 29.
Use 6 as the next digit of our solution. 
Result so far: 16.0
If we take 180 away from 209, we end up with 29.
Include the next digit (5) from the dividend after 29, then repeat: 295 / 30

Advancing to step 4:
The number 30 fits into 295 9 times, leaving a remainder of 25.
The next digit of our result is 9. 
Result so far: 169.0
Subtracting 270 from 295 leaves us with 25.
Grab the next digit (6) from the dividend, add it to 25, then carry on: 256 / 30

Let's proceed to step 5:
30 can be fit into 256 8 times, resulting in a remainder of 16.
Use 8 as the next digit of our solution. 
Result so far: 1698.0
Subtracting 240 from 256 leaves us with 16.
Take the next digit (7) from the dividend and append it to 16, then repeat: 167 / 30

Step 6:
30 goes into 167 5 times with a remainder of 17.
Record the quotient 5 as the next digit in the result. 
Result so far: 16985.0
The remainder is 17 after subtracting 150 from 167.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 7:
30 can be fit into 170 5 times, resulting in a remainder of 20.
The next digit of our result is 5. 
Result so far: 16985.5
Deduct 150 from 170 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 8:
200 divided by 30 is 6 with a remainder of 20.
Write down 6 as next digit of the result. 
Result so far: 16985.56
Deduct 180 from 200 and we're left with 20.
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 9:
200 divided by 30 is 6 with a remainder of 20.
The number 6 becomes the next digit in our result. 
Result so far: 16985.566
If we take 180 away from 200, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 16985.566, and the remainder is 0.002.