We're dividing 533321 by 25 
We're looking to find how many times 25 goes into 533321.

Step 1:
If we divide 5 by 25, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (3) from the dividend, add it to 5, then carry on: 53 / 25

Going ahead to step 2:
53 divided by 25 is 2 with a remainder of 3.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we subtract 50 from 53, we get 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 25

Moving on to step 3:
33 divided by 25 is 1 with a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 21.0
Deduct 25 from 33 and we're left with 8.
Append the next digit (3) from the dividend to 8 and continue with: 83 / 25

Moving on to step 4:
25 goes into 83 3 times with a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 213.0
Deduct 75 from 83 and we're left with 8.
Take the next digit (2) from the dividend and append it to 8, then repeat: 82 / 25

Going ahead to step 5:
25 goes into 82 3 times with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 2133.0
Subtract 75 from 82 to get 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 25

Moving on to step 6:
When dividing 71 by 25, we get 2 with a remainder of 21.
The number 2 becomes the next digit in our result. 
Result so far: 21332.0
If we take 50 away from 71, we end up 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.

Going ahead to step 7:
If we divide 210 by 25, we get 8 and a remainder of 10.
The number 8 becomes the next digit in our result. 
Result so far: 21332.8
The remainder is 10 after subtracting 200 from 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
100 divided by 25 is 4 with a remainder of 0.
The number 4 becomes the next digit in our result. 
Result so far: 21332.84
Subtracting 100 from 100 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 9:
25 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 21332.84
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 10:
When dividing 0 by 25, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 21332.84
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 21332.84 with a balance of 0.0.