255643 ÷ 15 
We want to figure out the number of times 255643 can be divided by 15.

On to step 1:
When dividing 2 by 15, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Include the next digit (5) from the dividend after 2, then repeat: 25 / 15

Step 2:
25 divided by 15 is 1 with a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 15 from 25 and we're left with 10.
Bring next digit (5) of the dividend behind the 10 and repeat the process: 105 / 15

On to step 3:
If we divide 105 by 15, we get 7 and a remainder of 0.
The next digit of our result is 7. 
Result so far: 17.0
Deduct 105 from 105 and we're left with 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 15

Step 4:
15 goes into 6 0 times with a remainder of 6.
The next digit of our result is 0. 
Result so far: 170.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 15

Advancing to step 5:
64 divided by 15 is 4 with a remainder of 4.
The next digit of our result is 4. 
Result so far: 1704.0
Subtracting 60 from 64 leaves us with 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 15

Step 6:
15 can be fit into 43 2 times, resulting in a remainder of 13.
Put 2 as the next digit of the answer. 
Result so far: 17042.0
Subtract 30 from 43 to get 13.
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:
When dividing 130 by 15, we get 8 with a remainder of 10.
The number 8 becomes the next digit in our result. 
Result so far: 17042.8
Subtract 120 from 130 to 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.

Step 8:
If we divide 100 by 15, we get 6 and a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 17042.86
Deduct 90 from 100 and we're left 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 9:
When dividing 100 by 15, we get 6 with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 17042.866
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 17042.866, and the remainder is 0.001.