We divide 338345 by 75
Our goal is to divide 338345 by 75.

Advancing to step 1:
When dividing 3 by 75, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 75

Moving on to step 2:
33 divided by 75 is 0 with a remainder of 33.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 33 leaves us with 33.
Append the next digit (8) from the dividend to 33 and continue with: 338 / 75

On to step 3:
75 goes into 338 4 times with a remainder of 38.
Write down 4 as next digit of the result. 
Result so far: 4.0
Deduct 300 from 338 and we're left with 38.
Include the next digit (3) from the dividend after 38, then repeat: 383 / 75

Let's proceed to step 4:
75 goes into 383 5 times with a remainder of 8.
The next digit of our result is 5. 
Result so far: 45.0
Deduct 375 from 383 and we're left with 8.
Take the next digit (4) from the dividend and append it to 8, then repeat: 84 / 75

On to step 5:
When dividing 84 by 75, we get 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 451.0
Subtract 75 from 84 to get 9.
Fetch the next digit (5) from the dividend, attach it to 9 and continue: 95 / 75

Step 6:
If we divide 95 by 75, we get 1 and a remainder of 20.
Write down 1 as next digit of the result. 
Result so far: 4511.0
Subtracting 75 from 95 leaves us 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.

Moving on to step 7:
If we divide 200 by 75, we get 2 and a remainder of 50.
Put 2 as the next digit of the answer. 
Result so far: 4511.2
Subtracting 150 from 200 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Step 8:
If we divide 500 by 75, we get 6 and a remainder of 50.
The next digit of our result is 6. 
Result so far: 4511.26
The remainder is 50 after subtracting 450 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 9:
If we divide 500 by 75, we get 6 and a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 4511.266
Deduct 450 from 500 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

In conclusion, the division gives 4511.266 with a balance of 0.005.