We look at the division of 338832 by 421 
We're looking to find how many times 421 goes into 338832.

Moving on to step 1:
The number 421 fits into 3 0 times, leaving a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (3) from the dividend, add it to 3, then carry on: 33 / 421

Advancing to step 2:
33 divided by 421 is 0 with a remainder of 33.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 33 after subtracting 0 from 33.
Append the next digit (8) from the dividend to 33 and continue with: 338 / 421

Going ahead to step 3:
421 goes into 338 0 times with a remainder of 338.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 338, we get 338.
Fetch the next digit (8) from the dividend, attach it to 338 and continue: 3388 / 421

Advancing to step 4:
421 can be fit into 3388 8 times, resulting in a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Subtracting 3368 from 3388 leaves us with 20.
Include the next digit (3) from the dividend after 20, then repeat: 203 / 421

Let's proceed to step 5:
421 can be fit into 203 0 times, resulting in a remainder of 203.
Write down 0 as next digit of the result. 
Result so far: 80.0
Deduct 0 from 203 and we're left with 203.
Grab the next digit (2) from the dividend, add it to 203, then carry on: 2032 / 421

On to step 6:
If we divide 2032 by 421, we get 4 and a remainder of 348.
The next digit of our result is 4. 
Result so far: 804.0
Deduct 1684 from 2032 and we're left with 348.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3480, and continue the process.

Going ahead to step 7:
421 goes into 3480 8 times with a remainder of 112.
Put 8 as the next digit of the answer. 
Result so far: 804.8
Subtract 3368 from 3480 to get 112.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1120, and continue the process.

Let's proceed to step 8:
421 can be fit into 1120 2 times, resulting in a remainder of 278.
Put 2 as the next digit of the answer. 
Result so far: 804.82
Subtracting 842 from 1120 leaves us with 278.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2780, and continue the process.

Advancing to step 9:
2780 divided by 421 is 6 with a remainder of 254.
Write down 6 as next digit of the result. 
Result so far: 804.826
The remainder is 254 after subtracting 2526 from 2780.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2540, and continue the process.

Let's proceed to step 10:
The number 421 fits into 2540 6 times, leaving a remainder of 14.
The number 6 becomes the next digit in our result. 
Result so far: 804.8266
Subtracting 2526 from 2540 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Our division results in 804.8266 with a remaining 0.00014.