177509 ÷ 30 
We're looking to find how many times 30 goes into 177509.

Moving on to step 1:
If we divide 1 by 30, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 30

Step 2:
When dividing 17 by 30, we get 0 with a remainder of 17.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Bring next digit (7) of the dividend behind the 17 and repeat the process: 177 / 30

Moving on to step 3:
30 goes into 177 5 times with a remainder of 27.
The next digit of our result is 5. 
Result so far: 5.0
If we take 150 away from 177, we end up with 27.
Include the next digit (5) from the dividend after 27, then repeat: 275 / 30

Let's proceed to step 4:
275 divided by 30 is 9 with a remainder of 5.
Use 9 as the next digit of our solution. 
Result so far: 59.0
Subtracting 270 from 275 leaves us with 5.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 30

On to step 5:
If we divide 50 by 30, we get 1 and a remainder of 20.
Put 1 as the next digit of the answer. 
Result so far: 591.0
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

Step 6:
209 divided by 30 is 6 with a remainder of 29.
The number 6 becomes the next digit in our result. 
Result so far: 5916.0
Deduct 180 from 209 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 7:
If we divide 290 by 30, we get 9 and a remainder of 20.
The number 9 becomes the next digit in our result. 
Result so far: 5916.9
If we take 270 away from 290, 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.

Step 8:
30 can be fit into 200 6 times, resulting in a remainder of 20.
The next digit of our result is 6. 
Result so far: 5916.96
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 9:
The number 30 fits into 200 6 times, leaving a remainder of 20.
Record the quotient 6 as the next digit in the result. 
Result so far: 5916.966
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 5916.966, and the remainder is 0.002.