21255 ÷ 17 
We're looking to find how many times 17 goes into 21255.

Moving on to step 1:
If we divide 2 by 17, we get 0 and a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 2 leaves us with 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 17

On to step 2:
When dividing 21 by 17, we get 1 with a remainder of 4.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 17 from 21, we get 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 17

On to step 3:
The number 17 fits into 42 2 times, leaving a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we subtract 34 from 42, we get 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 17

On to step 4:
17 goes into 85 5 times with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 125.0
Subtracting 85 from 85 leaves us with 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 17

Going ahead to step 5:
If we divide 5 by 17, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 1250.0
Subtract 0 from 5 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 6:
The number 17 fits into 50 2 times, leaving a remainder of 16.
The next digit of our result is 2. 
Result so far: 1250.2
If we take 34 away from 50, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 7:
The number 17 fits into 160 9 times, leaving a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 1250.29
Deduct 153 from 160 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
70 divided by 17 is 4 with a remainder of 2.
Write down 4 as next digit of the result. 
Result so far: 1250.294
If we take 68 away from 70, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 9:
If we divide 20 by 17, we get 1 and a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 1250.2941
If we subtract 17 from 20, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 10:
If we divide 30 by 17, we get 1 and a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 1250.29411
The remainder is 13 after subtracting 17 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The quotient of the division is 1250.29411, and the remainder is 1.3e-05.