583304 ÷ 9 
Our goal is to divide 583304 by 9.

Going ahead to step 1:
5 divided by 9 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 9

Let's proceed to step 2:
When dividing 58 by 9, we get 6 with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Deduct 54 from 58 and we're left with 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 9

Advancing to step 3:
The number 9 fits into 43 4 times, leaving a remainder of 7.
Write down 4 as next digit of the result. 
Result so far: 64.0
Subtracting 36 from 43 leaves us with 7.
Grab the next digit (3) from the dividend, add it to 7, then carry on: 73 / 9

Advancing to step 4:
If we divide 73 by 9, we get 8 and a remainder of 1.
The next digit of our result is 8. 
Result so far: 648.0
The remainder is 1 after subtracting 72 from 73.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 9

Let's proceed to step 5:
10 divided by 9 is 1 with a remainder of 1.
The next digit of our result is 1. 
Result so far: 6481.0
If we take 9 away from 10, we end up with 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 9

Going ahead to step 6:
9 goes into 14 1 times with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 64811.0
Deduct 9 from 14 and we're left 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.

Moving on to step 7:
When dividing 50 by 9, we get 5 with a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 64811.5
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.

Advancing to step 8:
If we divide 50 by 9, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 64811.55
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 64811.55, and the remainder is 0.005.