We divide 680513 by 15
We want to figure out the number of times 680513 can be divided by 15.

Advancing to step 1:
15 goes into 6 0 times with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 15

Moving on to step 2:
When dividing 68 by 15, we get 4 with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 4.0
Subtract 60 from 68 to get 8.
Include the next digit (0) from the dividend after 8, then repeat: 80 / 15

On to step 3:
When dividing 80 by 15, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 45.0
If we take 75 away from 80, we end up with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 15

On to step 4:
If we divide 55 by 15, we get 3 and a remainder of 10.
Put 3 as the next digit of the answer. 
Result so far: 453.0
If we subtract 45 from 55, we get 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 15

Step 5:
The number 15 fits into 101 6 times, leaving a remainder of 11.
Put 6 as the next digit of the answer. 
Result so far: 4536.0
If we take 90 away from 101, we end up with 11.
Take the next digit (3) from the dividend and append it to 11, then repeat: 113 / 15

Let's proceed to step 6:
The number 15 fits into 113 7 times, leaving a remainder of 8.
Use 7 as the next digit of our solution. 
Result so far: 45367.0
If we take 105 away from 113, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 7:
15 can be fit into 80 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 45367.5
Deduct 75 from 80 and we're left 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.

Let's proceed to step 8:
15 can be fit into 50 3 times, resulting in a remainder of 5.
Use 3 as the next digit of our solution. 
Result so far: 45367.53
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.

Let's proceed to step 9:
15 can be fit into 50 3 times, resulting in a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 45367.533
The remainder is 5 after subtracting 45 from 50.
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 45367.533, and the remainder is 0.0005.