We look at the division of 553566 by 65 
Let's see how many times 65 fits into 553566.

On to step 1:
When dividing 5 by 65, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 65

Let's proceed to step 2:
65 goes into 55 0 times with a remainder of 55.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 55 leaves us with 55.
Grab the next digit (3) from the dividend, add it to 55, then carry on: 553 / 65

Advancing to step 3:
553 divided by 65 is 8 with a remainder of 33.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Deduct 520 from 553 and we're left with 33.
Take the next digit (5) from the dividend and append it to 33, then repeat: 335 / 65

Let's proceed to step 4:
The number 65 fits into 335 5 times, leaving a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 85.0
Deduct 325 from 335 and we're left with 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 65

Step 5:
When dividing 106 by 65, we get 1 with a remainder of 41.
The next digit of our result is 1. 
Result so far: 851.0
Subtracting 65 from 106 leaves us with 41.
Include the next digit (6) from the dividend after 41, then repeat: 416 / 65

On to step 6:
If we divide 416 by 65, we get 6 and a remainder of 26.
Write down 6 as next digit of the result. 
Result so far: 8516.0
The remainder is 26 after subtracting 390 from 416.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 7:
260 divided by 65 is 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 8516.4
If we subtract 260 from 260, we 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.

Moving on to step 8:
If we divide 0 by 65, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 8516.4
Deduct 0 from 0 and we're left 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.

Advancing to step 9:
65 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 8516.4
Deduct 0 from 0 and we're left 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.

Our division results in 8516.4 with a remaining 0.0.