We look at the division of 583768 by 15 
We want to figure out the number of times 583768 can be divided by 15.

Moving on to step 1:
15 can be fit into 5 0 times, resulting in 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.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 15

Moving on to step 2:
The number 15 fits into 58 3 times, leaving a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Deduct 45 from 58 and we're left with 13.
Grab the next digit (3) from the dividend, add it to 13, then carry on: 133 / 15

Moving on to step 3:
15 can be fit into 133 8 times, resulting in a remainder of 13.
The next digit of our result is 8. 
Result so far: 38.0
Subtracting 120 from 133 leaves us with 13.
Append the next digit (7) from the dividend to 13 and continue with: 137 / 15

Advancing to step 4:
15 goes into 137 9 times with a remainder of 2.
The next digit of our result is 9. 
Result so far: 389.0
The remainder is 2 after subtracting 135 from 137.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 15

Step 5:
When dividing 26 by 15, we get 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 3891.0
The remainder is 11 after subtracting 15 from 26.
Fetch the next digit (8) from the dividend, attach it to 11 and continue: 118 / 15

Going ahead to step 6:
The number 15 fits into 118 7 times, leaving a remainder of 13.
The next digit of our result is 7. 
Result so far: 38917.0
The remainder is 13 after subtracting 105 from 118.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
15 can be fit into 130 8 times, resulting in a remainder of 10.
The number 8 becomes the next digit in our result. 
Result so far: 38917.8
Subtracting 120 from 130 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.

On to step 8:
If we divide 100 by 15, we get 6 and a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 38917.86
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.
Put 6 as the next digit of the answer. 
Result so far: 38917.866
Deduct 90 from 100 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.

The quotient of the division is 38917.866, and the remainder is 0.001.