We're dividing 338308 by 59 
Our goal is to divide 338308 by 59.

Going ahead to step 1:
59 can be fit into 3 0 times, resulting in a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 59

Step 2:
59 goes into 33 0 times with a remainder of 33.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 33, we get 33.
Take the next digit (8) from the dividend and append it to 33, then repeat: 338 / 59

Advancing to step 3:
59 can be fit into 338 5 times, resulting in a remainder of 43.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 295 from 338 and we're left with 43.
Append the next digit (3) from the dividend to 43 and continue with: 433 / 59

On to step 4:
433 divided by 59 is 7 with a remainder of 20.
Record the quotient 7 as the next digit in the result. 
Result so far: 57.0
Deduct 413 from 433 and we're left with 20.
Take the next digit (0) from the dividend and append it to 20, then repeat: 200 / 59

Advancing to step 5:
When dividing 200 by 59, we get 3 with a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 573.0
Subtract 177 from 200 to get 23.
Grab the next digit (8) from the dividend, add it to 23, then carry on: 238 / 59

Moving on to step 6:
59 goes into 238 4 times with a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 5734.0
Subtract 236 from 238 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
If we divide 20 by 59, we get 0 and a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 5734.0
Deduct 0 from 20 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.

Advancing to step 8:
If we divide 200 by 59, we get 3 and a remainder of 23.
Record the quotient 3 as the next digit in the result. 
Result so far: 5734.03
If we subtract 177 from 200, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 9:
230 divided by 59 is 3 with a remainder of 53.
Use 3 as the next digit of our solution. 
Result so far: 5734.033
Subtracting 177 from 230 leaves us with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

In conclusion, the division gives 5734.033 with a balance of 0.0053.