We're dividing 582175 by 15 
We're looking to find how many times 15 goes into 582175.

Step 1:
5 divided by 15 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 15

Moving on to step 2:
58 divided by 15 is 3 with a remainder of 13.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Deduct 45 from 58 and we're left with 13.
Fetch the next digit (2) from the dividend, attach it to 13 and continue: 132 / 15

On to step 3:
15 can be fit into 132 8 times, resulting in a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 38.0
Subtract 120 from 132 to get 12.
Grab the next digit (1) from the dividend, add it to 12, then carry on: 121 / 15

Going ahead to step 4:
If we divide 121 by 15, we get 8 and a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 388.0
The remainder is 1 after subtracting 120 from 121.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 15

Step 5:
When dividing 17 by 15, we get 1 with a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 3881.0
If we take 15 away from 17, we end up with 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 15

Going ahead to step 6:
15 goes into 25 1 times with a remainder of 10.
The next digit of our result is 1. 
Result so far: 38811.0
Subtract 15 from 25 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 7:
100 divided by 15 is 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 38811.6
If we take 90 away from 100, we end up 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:
When dividing 100 by 15, we get 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 38811.66
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 38811.66, and the remainder is 0.01.