633874 divided by 15 
We want to divide 633874 by 15.

Going ahead to step 1:
When dividing 6 by 15, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 15

Moving on to step 2:
When dividing 63 by 15, we get 4 with a remainder of 3.
The next digit of our result is 4. 
Result so far: 4.0
Deduct 60 from 63 and we're left with 3.
Take the next digit (3) from the dividend and append it to 3, then repeat: 33 / 15

Let's proceed to step 3:
15 can be fit into 33 2 times, resulting in a remainder of 3.
Use 2 as the next digit of our solution. 
Result so far: 42.0
If we take 30 away from 33, we end up with 3.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 15

Advancing to step 4:
38 divided by 15 is 2 with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 422.0
The remainder is 8 after subtracting 30 from 38.
Fetch the next digit (7) from the dividend, attach it to 8 and continue: 87 / 15

On to step 5:
If we divide 87 by 15, we get 5 and a remainder of 12.
Write down 5 as next digit of the result. 
Result so far: 4225.0
Subtract 75 from 87 to get 12.
Include the next digit (4) from the dividend after 12, then repeat: 124 / 15

Going ahead to step 6:
The number 15 fits into 124 8 times, leaving a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 42258.0
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.

Going ahead to step 7:
When dividing 40 by 15, we get 2 with a remainder of 10.
The next digit of our result is 2. 
Result so far: 42258.2
Subtracting 30 from 40 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.

Moving on to 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: 42258.26
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.

Moving on to step 9:
15 goes into 100 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 42258.266
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.

The quotient of the division is 42258.266, and the remainder is 0.001.