We're dividing 645881 by 15 
We're looking to find how many times 15 goes into 645881.

Advancing to step 1:
The number 15 fits into 6 0 times, leaving a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 15

Going ahead to step 2:
If we divide 64 by 15, we get 4 and a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
Subtract 60 from 64 to get 4.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 15

Step 3:
If we divide 45 by 15, we get 3 and a remainder of 0.
Put 3 as the next digit of the answer. 
Result so far: 43.0
If we take 45 away from 45, we end up with 0.
Grab the next digit (8) from the dividend, add it to 0, then carry on: 8 / 15

Going ahead to step 4:
8 divided by 15 is 0 with a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 430.0
The remainder is 8 after subtracting 0 from 8.
Append the next digit (8) from the dividend to 8 and continue with: 88 / 15

Moving on to step 5:
15 can be fit into 88 5 times, resulting in a remainder of 13.
Write down 5 as next digit of the result. 
Result so far: 4305.0
If we subtract 75 from 88, we get 13.
Include the next digit (1) from the dividend after 13, then repeat: 131 / 15

Moving on to step 6:
131 divided by 15 is 8 with a remainder of 11.
Put 8 as the next digit of the answer. 
Result so far: 43058.0
If we subtract 120 from 131, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 7:
The number 15 fits into 110 7 times, leaving a remainder of 5.
Write down 7 as next digit of the result. 
Result so far: 43058.7
Subtracting 105 from 110 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
50 divided by 15 is 3 with a remainder of 5.
Record the quotient 3 as the next digit in the result. 
Result so far: 43058.73
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 9:
If we divide 50 by 15, we get 3 and a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 43058.733
Subtract 45 from 50 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 43058.733, and the remainder is 0.0005.