We look at the division of 6584 by 9 
We want to divide 6584 by 9.

Step 1:
9 can be fit into 6 0 times, resulting in a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (5) from the dividend, add it to 6, then carry on: 65 / 9

Moving on to step 2:
9 goes into 65 7 times with a remainder of 2.
The next digit of our result is 7. 
Result so far: 7.0
Subtract 63 from 65 to get 2.
Include the next digit (8) from the dividend after 2, then repeat: 28 / 9

Let's proceed to step 3:
When dividing 28 by 9, we get 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 73.0
If we take 27 away from 28, we end up with 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 9

Let's proceed to step 4:
If we divide 14 by 9, we get 1 and a remainder of 5.
The next digit of our result is 1. 
Result so far: 731.0
Subtract 9 from 14 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 5:
The number 9 fits into 50 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 731.5
Subtracting 45 from 50 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 6:
The number 9 fits into 50 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 731.55
If we subtract 45 from 50, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Our division results in 731.55 with a remaining 0.005.