21278 ÷ 14 
Our goal is to divide 21278 by 14.

Going ahead to step 1:
The number 14 fits into 2 0 times, leaving 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.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 14

Let's proceed to step 2:
The number 14 fits into 21 1 times, leaving a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 14 from 21, we get 7.
Take the next digit (2) from the dividend and append it to 7, then repeat: 72 / 14

Moving on to step 3:
If we divide 72 by 14, we get 5 and a remainder of 2.
The next digit of our result is 5. 
Result so far: 15.0
If we subtract 70 from 72, we get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 14

Advancing to step 4:
If we divide 27 by 14, we get 1 and a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 151.0
Subtract 14 from 27 to get 13.
Bring next digit (8) of the dividend behind the 13 and repeat the process: 138 / 14

Advancing to step 5:
14 can be fit into 138 9 times, resulting in a remainder of 12.
Record the quotient 9 as the next digit in the result. 
Result so far: 1519.0
Subtracting 126 from 138 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 6:
If we divide 120 by 14, we get 8 and a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 1519.8
The remainder is 8 after subtracting 112 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 7:
The number 14 fits into 80 5 times, leaving a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 1519.85
Deduct 70 from 80 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.

Advancing to step 8:
14 can be fit into 100 7 times, resulting in a remainder of 2.
The next digit of our result is 7. 
Result so far: 1519.857
The remainder is 2 after subtracting 98 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 9:
14 goes into 20 1 times with a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 1519.8571
The remainder is 6 after subtracting 14 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 10:
If we divide 60 by 14, we get 4 and a remainder of 4.
The next digit of our result is 4. 
Result so far: 1519.85714
Subtract 56 from 60 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 11:
When dividing 40 by 14, we get 2 with a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 1519.857142
If we subtract 28 from 40, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 12:
When dividing 120 by 14, we get 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 1519.8571428
Deduct 112 from 120 and we're left 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 13:
When dividing 80 by 14, we get 5 with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 1519.85714285
Subtracting 70 from 80 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.

After the division, we end up with 1519.85714285 and a remainder of 1e-08.