We're dividing 625834 by 33 
We want to figure out the number of times 625834 can be divided by 33.

Going ahead to step 1:
When dividing 6 by 33, we get 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Bring next digit (2) of the dividend behind the 6 and repeat the process: 62 / 33

On to step 2:
33 goes into 62 1 times with a remainder of 29.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 33 away from 62, we end up with 29.
Append the next digit (5) from the dividend to 29 and continue with: 295 / 33

Advancing to step 3:
When dividing 295 by 33, we get 8 with a remainder of 31.
Write down 8 as next digit of the result. 
Result so far: 18.0
Deduct 264 from 295 and we're left with 31.
Fetch the next digit (8) from the dividend, attach it to 31 and continue: 318 / 33

Step 4:
When dividing 318 by 33, we get 9 with a remainder of 21.
Put 9 as the next digit of the answer. 
Result so far: 189.0
The remainder is 21 after subtracting 297 from 318.
Append the next digit (3) from the dividend to 21 and continue with: 213 / 33

Step 5:
33 can be fit into 213 6 times, resulting in a remainder of 15.
Use 6 as the next digit of our solution. 
Result so far: 1896.0
If we take 198 away from 213, we end up with 15.
Include the next digit (4) from the dividend after 15, then repeat: 154 / 33

Moving on to step 6:
33 can be fit into 154 4 times, resulting in a remainder of 22.
The number 4 becomes the next digit in our result. 
Result so far: 18964.0
The remainder is 22 after subtracting 132 from 154.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 7:
If we divide 220 by 33, we get 6 and a remainder of 22.
Write down 6 as next digit of the result. 
Result so far: 18964.6
If we take 198 away from 220, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 8:
33 can be fit into 220 6 times, resulting in a remainder of 22.
Put 6 as the next digit of the answer. 
Result so far: 18964.66
Subtract 198 from 220 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

In conclusion, the division gives 18964.66 with a balance of 0.022.