We divide 338635 by 53
We're looking to find how many times 53 goes into 338635.

Step 1:
53 can be fit into 3 0 times, resulting in a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Include the next digit (3) from the dividend after 3, then repeat: 33 / 53

On to step 2:
53 goes into 33 0 times with a remainder of 33.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 33 after subtracting 0 from 33.
Include the next digit (8) from the dividend after 33, then repeat: 338 / 53

Moving on to step 3:
If we divide 338 by 53, we get 6 and a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 318 from 338, we get 20.
Take the next digit (6) from the dividend and append it to 20, then repeat: 206 / 53

Advancing to step 4:
The number 53 fits into 206 3 times, leaving a remainder of 47.
The next digit of our result is 3. 
Result so far: 63.0
Subtract 159 from 206 to get 47.
Include the next digit (3) from the dividend after 47, then repeat: 473 / 53

Step 5:
When dividing 473 by 53, we get 8 with a remainder of 49.
Record the quotient 8 as the next digit in the result. 
Result so far: 638.0
If we take 424 away from 473, we end up with 49.
Include the next digit (5) from the dividend after 49, then repeat: 495 / 53

Step 6:
495 divided by 53 is 9 with a remainder of 18.
The next digit of our result is 9. 
Result so far: 6389.0
Subtract 477 from 495 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 7:
180 divided by 53 is 3 with a remainder of 21.
Use 3 as the next digit of our solution. 
Result so far: 6389.3
Subtracting 159 from 180 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 8:
When dividing 210 by 53, we get 3 with a remainder of 51.
The number 3 becomes the next digit in our result. 
Result so far: 6389.33
Subtract 159 from 210 to get 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

The final outcome is 6389.33, with a leftover of 0.051.