585331 divided by 9 
Our goal is to divide 585331 by 9.

Step 1:
5 divided by 9 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 9

Advancing to step 2:
If we divide 58 by 9, we get 6 and a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 6.0
The remainder is 4 after subtracting 54 from 58.
Fetch the next digit (5) from the dividend, attach it to 4 and continue: 45 / 9

On to step 3:
9 can be fit into 45 5 times, resulting in a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 65.0
Subtracting 45 from 45 leaves us with 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 9

On to step 4:
9 goes into 3 0 times with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 650.0
Deduct 0 from 3 and we're left with 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 9

Advancing to step 5:
If we divide 33 by 9, we get 3 and a remainder of 6.
The number 3 becomes the next digit in our result. 
Result so far: 6503.0
Subtracting 27 from 33 leaves us with 6.
Include the next digit (1) from the dividend after 6, then repeat: 61 / 9

Let's proceed to step 6:
9 goes into 61 6 times with a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 65036.0
Subtract 54 from 61 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 7:
When dividing 70 by 9, we get 7 with a remainder of 7.
Use 7 as the next digit of our solution. 
Result so far: 65036.7
If we subtract 63 from 70, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 8:
If we divide 70 by 9, we get 7 and a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 65036.77
Subtracting 63 from 70 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The quotient of the division is 65036.77, and the remainder is 0.007.