65564 ÷ 3 
Our goal is to divide 65564 by 3.

Advancing to step 1:
6 divided by 3 is 2 with a remainder of 0.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we subtract 6 from 6, we get 0.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 3

Let's proceed to step 2:
5 divided by 3 is 1 with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 21.0
If we take 3 away from 5, we end up with 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 3

Advancing to step 3:
When dividing 25 by 3, we get 8 with a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 218.0
If we take 24 away from 25, we end up with 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 3

Moving on to step 4:
When dividing 16 by 3, we get 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 2185.0
The remainder is 1 after subtracting 15 from 16.
Append the next digit (4) from the dividend to 1 and continue with: 14 / 3

Moving on to step 5:
When dividing 14 by 3, we get 4 with a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 21854.0
Deduct 12 from 14 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 6:
When dividing 20 by 3, we get 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 21854.6
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
When dividing 20 by 3, we get 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 21854.66
Subtracting 18 from 20 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

After the division, we end up with 21854.66 and a remainder of 0.002.