We look at the division of 585369 by 16 
We want to divide 585369 by 16.

Step 1:
16 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 16

On to step 2:
When dividing 58 by 16, we get 3 with a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 3.0
If we take 48 away from 58, we end up with 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 16

Let's proceed to step 3:
16 can be fit into 105 6 times, resulting in a remainder of 9.
Put 6 as the next digit of the answer. 
Result so far: 36.0
If we subtract 96 from 105, we get 9.
Fetch the next digit (3) from the dividend, attach it to 9 and continue: 93 / 16

On to step 4:
The number 16 fits into 93 5 times, leaving a remainder of 13.
Use 5 as the next digit of our solution. 
Result so far: 365.0
Subtracting 80 from 93 leaves us with 13.
Include the next digit (6) from the dividend after 13, then repeat: 136 / 16

On to step 5:
When dividing 136 by 16, we get 8 with a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 3658.0
The remainder is 8 after subtracting 128 from 136.
Append the next digit (9) from the dividend to 8 and continue with: 89 / 16

On to step 6:
If we divide 89 by 16, we get 5 and a remainder of 9.
Record the quotient 5 as the next digit in the result. 
Result so far: 36585.0
Subtracting 80 from 89 leaves us 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.

Step 7:
When dividing 90 by 16, we get 5 with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 36585.5
Deduct 80 from 90 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
The number 16 fits into 100 6 times, leaving a remainder of 4.
The next digit of our result is 6. 
Result so far: 36585.56
Subtracting 96 from 100 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.

Let's proceed to step 9:
16 can be fit into 40 2 times, resulting in a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 36585.562
Deduct 32 from 40 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.

On to step 10:
When dividing 80 by 16, we get 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 36585.5625
Subtracting 80 from 80 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 11:
The number 16 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 36585.5625
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 12:
16 goes into 0 0 times with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 36585.5625
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 36585.5625, and the remainder is 0.0.