We look at the division of 583645 by 16 
We're looking to find how many times 16 goes into 583645.

On to step 1:
5 divided by 16 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 16

Let's proceed to step 2:
If we divide 58 by 16, we get 3 and a remainder of 10.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 10 after subtracting 48 from 58.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 16

Going ahead to step 3:
When dividing 103 by 16, we get 6 with a remainder of 7.
Use 6 as the next digit of our solution. 
Result so far: 36.0
Deduct 96 from 103 and we're left with 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 16

Moving on to step 4:
If we divide 76 by 16, we get 4 and a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 364.0
The remainder is 12 after subtracting 64 from 76.
Fetch the next digit (4) from the dividend, attach it to 12 and continue: 124 / 16

Going ahead to step 5:
If we divide 124 by 16, we get 7 and a remainder of 12.
Record the quotient 7 as the next digit in the result. 
Result so far: 3647.0
If we subtract 112 from 124, we get 12.
Append the next digit (5) from the dividend to 12 and continue with: 125 / 16

Let's proceed to step 6:
When dividing 125 by 16, we get 7 with a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 36477.0
Deduct 112 from 125 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 7:
16 goes into 130 8 times with a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 36477.8
The remainder is 2 after subtracting 128 from 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
16 goes into 20 1 times with a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 36477.81
Subtract 16 from 20 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 9:
When dividing 40 by 16, we get 2 with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 36477.812
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.

Going ahead to step 10:
80 divided by 16 is 5 with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 36477.8125
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 11:
0 divided by 16 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 36477.8125
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 12:
16 goes into 0 0 times with a remainder of 0.
The next digit of our result is 0. 
Result so far: 36477.8125
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.

After the division, we end up with 36477.8125 and a remainder of 0.0.