Let's divide 586581 by 16
We want to divide 586581 by 16.

Moving on to step 1:
The number 16 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Grab the next digit (8) from the dividend, add it to 5, then carry on: 58 / 16

Step 2:
If we divide 58 by 16, we get 3 and a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtracting 48 from 58 leaves us with 10.
Include the next digit (6) from the dividend after 10, then repeat: 106 / 16

Step 3:
106 divided by 16 is 6 with a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 36.0
If we take 96 away from 106, we end up with 10.
Take the next digit (5) from the dividend and append it to 10, then repeat: 105 / 16

Moving on to step 4:
16 can be fit into 105 6 times, resulting in a remainder of 9.
Write down 6 as next digit of the result. 
Result so far: 366.0
The remainder is 9 after subtracting 96 from 105.
Fetch the next digit (8) from the dividend, attach it to 9 and continue: 98 / 16

Going ahead to step 5:
16 goes into 98 6 times with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 3666.0
If we subtract 96 from 98, we get 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 16

On to step 6:
21 divided by 16 is 1 with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 36661.0
If we take 16 away from 21, we end up 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.

Step 7:
16 can be fit into 50 3 times, resulting in a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 36661.3
Deduct 48 from 50 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
When dividing 20 by 16, we get 1 with a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 36661.31
If we take 16 away from 20, 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.

Advancing to step 9:
16 goes into 40 2 times with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 36661.312
Subtracting 32 from 40 leaves us 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.

Step 10:
16 goes into 80 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 36661.3125
Subtract 80 from 80 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.

Going ahead to step 11:
If we divide 0 by 16, we get 0 and a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 36661.3125
Subtracting 0 from 0 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.

Let's proceed to step 12:
When dividing 0 by 16, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 36661.3125
If we subtract 0 from 0, we 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.

Our division results in 36661.3125 with a remaining 0.0.