We look at the division of 641717 by 15 
We're looking to find how many times 15 goes into 641717.

Moving on to step 1:
If we divide 6 by 15, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 15

Moving on to step 2:
When dividing 64 by 15, we get 4 with a remainder of 4.
The next digit of our result is 4. 
Result so far: 4.0
Subtract 60 from 64 to get 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 15

Let's proceed to step 3:
15 can be fit into 41 2 times, resulting in a remainder of 11.
Use 2 as the next digit of our solution. 
Result so far: 42.0
If we take 30 away from 41, we end up with 11.
Take the next digit (7) from the dividend and append it to 11, then repeat: 117 / 15

Step 4:
The number 15 fits into 117 7 times, leaving a remainder of 12.
Put 7 as the next digit of the answer. 
Result so far: 427.0
Deduct 105 from 117 and we're left with 12.
Append the next digit (1) from the dividend to 12 and continue with: 121 / 15

On to step 5:
If we divide 121 by 15, we get 8 and a remainder of 1.
The next digit of our result is 8. 
Result so far: 4278.0
The remainder is 1 after subtracting 120 from 121.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 15

Advancing to step 6:
If we divide 17 by 15, we get 1 and a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 42781.0
Subtract 15 from 17 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 7:
20 divided by 15 is 1 with a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 42781.1
If we take 15 away from 20, we end up 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.

Going ahead to step 8:
The number 15 fits into 50 3 times, leaving a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 42781.13
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.

Moving on to step 9:
50 divided by 15 is 3 with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 42781.133
If we take 45 away from 50, we end up 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.

In conclusion, the division gives 42781.133 with a balance of 0.0005.