We look at the division of 684538 by 15 
Let's see how many times 15 fits into 684538.

Going ahead to step 1:
The number 15 fits into 6 0 times, leaving 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.
Grab the next digit (8) from the dividend, add it to 6, then carry on: 68 / 15

Going ahead to step 2:
When dividing 68 by 15, we get 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
The remainder is 8 after subtracting 60 from 68.
Grab the next digit (4) from the dividend, add it to 8, then carry on: 84 / 15

Moving on to step 3:
15 can be fit into 84 5 times, resulting in a remainder of 9.
Use 5 as the next digit of our solution. 
Result so far: 45.0
Deduct 75 from 84 and we're left with 9.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 15

On to step 4:
When dividing 95 by 15, we get 6 with a remainder of 5.
Write down 6 as next digit of the result. 
Result so far: 456.0
If we take 90 away from 95, we end up with 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 15

Step 5:
15 goes into 53 3 times with a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 4563.0
Subtracting 45 from 53 leaves us with 8.
Include the next digit (8) from the dividend after 8, then repeat: 88 / 15

Advancing to step 6:
15 can be fit into 88 5 times, resulting in a remainder of 13.
Record the quotient 5 as the next digit in the result. 
Result so far: 45635.0
The remainder is 13 after subtracting 75 from 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 7:
15 can be fit into 130 8 times, resulting in a remainder of 10.
Use 8 as the next digit of our solution. 
Result so far: 45635.8
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.

Let's proceed 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: 45635.86
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.

Going ahead to step 9:
When dividing 100 by 15, we get 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 45635.866
The remainder is 10 after subtracting 90 from 100.
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 45635.866, and the remainder is 0.001.