174128 ÷ 30 
We're looking to find how many times 30 goes into 174128.

Going ahead to step 1:
The number 30 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 30

Advancing to step 2:
When dividing 17 by 30, we get 0 with a remainder of 17.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Fetch the next digit (4) from the dividend, attach it to 17 and continue: 174 / 30

Advancing to step 3:
When dividing 174 by 30, we get 5 with a remainder of 24.
The next digit of our result is 5. 
Result so far: 5.0
Subtracting 150 from 174 leaves us with 24.
Take the next digit (1) from the dividend and append it to 24, then repeat: 241 / 30

Going ahead to step 4:
30 goes into 241 8 times with a remainder of 1.
Write down 8 as next digit of the result. 
Result so far: 58.0
If we take 240 away from 241, we end up with 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 30

Let's proceed to step 5:
12 divided by 30 is 0 with a remainder of 12.
The next digit of our result is 0. 
Result so far: 580.0
The remainder is 12 after subtracting 0 from 12.
Grab the next digit (8) from the dividend, add it to 12, then carry on: 128 / 30

Step 6:
The number 30 fits into 128 4 times, leaving a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 5804.0
Subtract 120 from 128 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 7:
30 goes into 80 2 times with a remainder of 20.
Record the quotient 2 as the next digit in the result. 
Result so far: 5804.2
Subtract 60 from 80 to 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.

Advancing to step 8:
If we divide 200 by 30, we get 6 and a remainder of 20.
Put 6 as the next digit of the answer. 
Result so far: 5804.26
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:
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: 5804.266
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.

The final result is 5804.266 with a remainder of 0.002.