We're dividing 125824 by 15 
Let's see how many times 15 fits into 125824.

Moving on to step 1:
15 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 15

On to step 2:
The number 15 fits into 12 0 times, leaving a remainder of 12.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 12 to get 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 15

On to step 3:
The number 15 fits into 125 8 times, leaving a remainder of 5.
The next digit of our result is 8. 
Result so far: 8.0
Subtract 120 from 125 to get 5.
Grab the next digit (8) from the dividend, add it to 5, then carry on: 58 / 15

Let's proceed to step 4:
58 divided by 15 is 3 with a remainder of 13.
Write down 3 as next digit of the result. 
Result so far: 83.0
If we take 45 away from 58, we end up with 13.
Fetch the next digit (2) from the dividend, attach it to 13 and continue: 132 / 15

Going ahead to step 5:
15 goes into 132 8 times with a remainder of 12.
The next digit of our result is 8. 
Result so far: 838.0
If we subtract 120 from 132, we get 12.
Take the next digit (4) from the dividend and append it to 12, then repeat: 124 / 15

Going ahead to step 6:
15 goes into 124 8 times with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 8388.0
Subtract 120 from 124 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.

Step 7:
The number 15 fits into 40 2 times, leaving a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 8388.2
Deduct 30 from 40 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.

On to step 8:
15 can be fit into 100 6 times, resulting in a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 8388.26
If we subtract 90 from 100, we 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.

Step 9:
100 divided by 15 is 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 8388.266
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 8388.266, and the remainder is 0.001.