We're dividing 233566 by 3 
We want to figure out the number of times 233566 can be divided by 3.

On to step 1:
The number 3 fits into 2 0 times, leaving a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 3

Going ahead to step 2:
When dividing 23 by 3, we get 7 with a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
If we take 21 away from 23, we end up with 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 3

Advancing to step 3:
The number 3 fits into 23 7 times, leaving a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 77.0
Subtracting 21 from 23 leaves us with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 3

Let's proceed to step 4:
3 can be fit into 25 8 times, resulting in a remainder of 1.
Write down 8 as next digit of the result. 
Result so far: 778.0
Deduct 24 from 25 and we're left with 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 3

Let's proceed to step 5:
The number 3 fits into 16 5 times, leaving a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 7785.0
Subtract 15 from 16 to get 1.
Grab the next digit (6) from the dividend, add it to 1, then carry on: 16 / 3

On to step 6:
3 goes into 16 5 times with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 77855.0
Subtract 15 from 16 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
3 goes into 10 3 times with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 77855.3
Subtracting 9 from 10 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 8:
10 divided by 3 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 77855.33
Deduct 9 from 10 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 77855.33 and a remainder of 0.001.