We look at the division of 584441 by 9 
We're looking to find how many times 9 goes into 584441.

Advancing to step 1:
If we divide 5 by 9, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Fetch the next digit (8) from the dividend, attach it to 5 and continue: 58 / 9

Moving on to step 2:
58 divided by 9 is 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtracting 54 from 58 leaves us with 4.
Take the next digit (4) from the dividend and append it to 4, then repeat: 44 / 9

Advancing to step 3:
9 can be fit into 44 4 times, resulting in a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 64.0
If we subtract 36 from 44, we get 8.
Fetch the next digit (4) from the dividend, attach it to 8 and continue: 84 / 9

Let's proceed to step 4:
9 goes into 84 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 649.0
If we take 81 away from 84, we end up with 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 9

Going ahead to step 5:
9 can be fit into 34 3 times, resulting in a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 6493.0
If we take 27 away from 34, we end up with 7.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 9

Moving on to step 6:
If we divide 71 by 9, we get 7 and a remainder of 8.
Write down 7 as next digit of the result. 
Result so far: 64937.0
The remainder is 8 after subtracting 63 from 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 7:
When dividing 80 by 9, we get 8 with a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 64937.8
Subtracting 72 from 80 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 8:
80 divided by 9 is 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 64937.88
Deduct 72 from 80 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

After the division, we end up with 64937.88 and a remainder of 0.008.