488563 ÷ 15 
Our goal is to divide 488563 by 15.

On to step 1:
15 goes into 4 0 times with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (8) from the dividend after 4, then repeat: 48 / 15

Step 2:
The number 15 fits into 48 3 times, leaving a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtracting 45 from 48 leaves us with 3.
Include the next digit (8) from the dividend after 3, then repeat: 38 / 15

Let's proceed to step 3:
15 can be fit into 38 2 times, resulting in a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 32.0
Subtracting 30 from 38 leaves us with 8.
Grab the next digit (5) from the dividend, add it to 8, then carry on: 85 / 15

Advancing to step 4:
If we divide 85 by 15, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 325.0
Deduct 75 from 85 and we're left with 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 15

Moving on to step 5:
106 divided by 15 is 7 with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 3257.0
Subtract 105 from 106 to get 1.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 15

On to step 6:
15 goes into 13 0 times with a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 32570.0
Subtracting 0 from 13 leaves us 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.

Advancing to step 7:
130 divided by 15 is 8 with a remainder of 10.
Write down 8 as next digit of the result. 
Result so far: 32570.8
Deduct 120 from 130 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.

Going ahead to step 8:
15 can be fit into 100 6 times, resulting in a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 32570.86
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 9:
100 divided by 15 is 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 32570.866
Subtracting 90 from 100 leaves us 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.

The quotient of the division is 32570.866, and the remainder is 0.001.