338604 divided by 65 
We're looking to find how many times 65 goes into 338604.

Let's proceed to step 1:
If we divide 3 by 65, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 65

Going ahead to step 2:
65 can be fit into 33 0 times, resulting in a remainder of 33.
Put 0 as the next digit of the answer. 
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 / 65

On to step 3:
338 divided by 65 is 5 with a remainder of 13.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Deduct 325 from 338 and we're left with 13.
Take the next digit (6) from the dividend and append it to 13, then repeat: 136 / 65

Let's proceed to step 4:
65 goes into 136 2 times with a remainder of 6.
Write down 2 as next digit of the result. 
Result so far: 52.0
The remainder is 6 after subtracting 130 from 136.
Grab the next digit (0) from the dividend, add it to 6, then carry on: 60 / 65

On to step 5:
65 goes into 60 0 times with a remainder of 60.
Use 0 as the next digit of our solution. 
Result so far: 520.0
Deduct 0 from 60 and we're left with 60.
Grab the next digit (4) from the dividend, add it to 60, then carry on: 604 / 65

On to step 6:
If we divide 604 by 65, we get 9 and a remainder of 19.
The number 9 becomes the next digit in our result. 
Result so far: 5209.0
Subtract 585 from 604 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 7:
65 can be fit into 190 2 times, resulting in a remainder of 60.
Write down 2 as next digit of the result. 
Result so far: 5209.2
If we take 130 away from 190, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 8:
600 divided by 65 is 9 with a remainder of 15.
The next digit of our result is 9. 
Result so far: 5209.29
The remainder is 15 after subtracting 585 from 600.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 9:
The number 65 fits into 150 2 times, leaving a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 5209.292
Subtracting 130 from 150 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.

On to step 10:
65 goes into 200 3 times with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 5209.2923
Subtracting 195 from 200 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
50 divided by 65 is 0 with a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 5209.2923
Deduct 0 from 50 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.

Moving on to step 12:
If we divide 500 by 65, we get 7 and a remainder of 45.
Record the quotient 7 as the next digit in the result. 
Result so far: 5209.292307
Subtract 455 from 500 to get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

On to step 13:
If we divide 450 by 65, we get 6 and a remainder of 60.
The number 6 becomes the next digit in our result. 
Result so far: 5209.2923076
Deduct 390 from 450 and we're left with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Moving on to step 14:
The number 65 fits into 600 9 times, leaving a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 5209.29230769
Subtracting 585 from 600 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

In conclusion, the division gives 5209.29230769 with a balance of 1.5e-08.