585584 ÷ 13 
Our goal is to divide 585584 by 13.

Moving on to step 1:
The number 13 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 13

On to step 2:
The number 13 fits into 58 4 times, leaving a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 4.0
If we subtract 52 from 58, we get 6.
Grab the next digit (5) from the dividend, add it to 6, then carry on: 65 / 13

Let's proceed to step 3:
13 can be fit into 65 5 times, resulting in a remainder of 0.
Put 5 as the next digit of the answer. 
Result so far: 45.0
Subtracting 65 from 65 leaves us with 0.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 13

Going ahead to step 4:
5 divided by 13 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 450.0
If we take 0 away from 5, we end up with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 13

Let's proceed to step 5:
58 divided by 13 is 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 4504.0
Subtracting 52 from 58 leaves us with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 13

Going ahead to step 6:
When dividing 64 by 13, we get 4 with a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 45044.0
Subtract 52 from 64 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 7:
13 goes into 120 9 times with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 45044.9
Deduct 117 from 120 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 8:
The number 13 fits into 30 2 times, leaving a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 45044.92
If we take 26 away from 30, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
13 can be fit into 40 3 times, resulting in a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 45044.923
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 10:
13 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 45044.923
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 11:
If we divide 100 by 13, we get 7 and a remainder of 9.
The next digit of our result is 7. 
Result so far: 45044.92307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 12:
90 divided by 13 is 6 with a remainder of 12.
The next digit of our result is 6. 
Result so far: 45044.923076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 13:
13 goes into 120 9 times with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 45044.9230769
Subtracting 117 from 120 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 14:
30 divided by 13 is 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 45044.92307692
Subtracting 26 from 30 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 45044.92307692, and the remainder is 4e-09.