We look at the division of 585838 by 16 
Let's see how many times 16 fits into 585838.

Advancing to step 1:
16 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (8) from the dividend, add it to 5, then carry on: 58 / 16

Advancing to step 2:
16 goes into 58 3 times with a remainder of 10.
The next digit of our result is 3. 
Result so far: 3.0
Subtracting 48 from 58 leaves us with 10.
Take the next digit (5) from the dividend and append it to 10, then repeat: 105 / 16

Advancing to step 3:
105 divided by 16 is 6 with a remainder of 9.
Record the quotient 6 as the next digit in the result. 
Result so far: 36.0
Deduct 96 from 105 and we're left with 9.
Append the next digit (8) from the dividend to 9 and continue with: 98 / 16

Let's proceed to step 4:
If we divide 98 by 16, we get 6 and a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 366.0
If we take 96 away from 98, we end up with 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 16

On to step 5:
The number 16 fits into 23 1 times, leaving a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 3661.0
Deduct 16 from 23 and we're left with 7.
Grab the next digit (8) from the dividend, add it to 7, then carry on: 78 / 16

On to step 6:
The number 16 fits into 78 4 times, leaving a remainder of 14.
The number 4 becomes the next digit in our result. 
Result so far: 36614.0
The remainder is 14 after subtracting 64 from 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 7:
140 divided by 16 is 8 with a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 36614.8
Deduct 128 from 140 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 8:
16 goes into 120 7 times with a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 36614.87
If we subtract 112 from 120, we get 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 9:
80 divided by 16 is 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 36614.875
Deduct 80 from 80 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.

Moving on to step 10:
16 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 36614.875
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 11:
16 can be fit into 0 0 times, resulting in a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 36614.875
Subtract 0 from 0 to get 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 final result is 36614.875 with a remainder of 0.0.