We look at the division of 75338 by 30 
We're looking to find how many times 30 goes into 75338.

Let's proceed to step 1:
7 divided by 30 is 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 30

Step 2:
30 goes into 75 2 times with a remainder of 15.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
The remainder is 15 after subtracting 60 from 75.
Bring next digit (3) of the dividend behind the 15 and repeat the process: 153 / 30

Let's proceed to step 3:
When dividing 153 by 30, we get 5 with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 25.0
Subtract 150 from 153 to get 3.
Include the next digit (3) from the dividend after 3, then repeat: 33 / 30

Advancing to step 4:
30 goes into 33 1 times with a remainder of 3.
The next digit of our result is 1. 
Result so far: 251.0
If we take 30 away from 33, we end up with 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 30

Let's proceed to step 5:
When dividing 38 by 30, we get 1 with a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 2511.0
If we subtract 30 from 38, we 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.

Advancing to step 6:
30 goes into 80 2 times with a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 2511.2
The remainder is 20 after subtracting 60 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 7:
30 can be fit into 200 6 times, resulting in a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 2511.26
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.

Going ahead to step 8:
30 goes into 200 6 times with a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 2511.266
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.

The final result is 2511.266 with a remainder of 0.002.