We divide 127116 by 21
We want to figure out the number of times 127116 can be divided by 21.

Moving on to step 1:
21 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 21

Step 2:
If we divide 12 by 21, we get 0 and a remainder of 12.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 12 to get 12.
Include the next digit (7) from the dividend after 12, then repeat: 127 / 21

On to step 3:
21 goes into 127 6 times with a remainder of 1.
Write down 6 as next digit of the result. 
Result so far: 6.0
Deduct 126 from 127 and we're left with 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 21

Moving on to step 4:
21 can be fit into 11 0 times, resulting in a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 60.0
If we subtract 0 from 11, we get 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 21

Step 5:
21 goes into 111 5 times with a remainder of 6.
Record the quotient 5 as the next digit in the result. 
Result so far: 605.0
The remainder is 6 after subtracting 105 from 111.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 21

On to step 6:
21 goes into 66 3 times with a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 6053.0
If we subtract 63 from 66, 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.

Going ahead to step 7:
If we divide 30 by 21, we get 1 and a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 6053.1
Subtract 21 from 30 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 8:
21 goes into 90 4 times with a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 6053.14
Subtract 84 from 90 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 9:
When dividing 60 by 21, we get 2 with a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 6053.142
If we subtract 42 from 60, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 10:
If we divide 180 by 21, we get 8 and a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 6053.1428
If we subtract 168 from 180, 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.

On to step 11:
When dividing 120 by 21, we get 5 with a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 6053.14285
If we subtract 105 from 120, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 12:
If we divide 150 by 21, we get 7 and a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 6053.142857
The remainder is 3 after subtracting 147 from 150.
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 13:
21 goes into 30 1 times with a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 6053.1428571
Subtracting 21 from 30 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 14:
21 can be fit into 90 4 times, resulting in a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 6053.14285714
If we take 84 away from 90, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

The quotient of the division is 6053.14285714, and the remainder is 6e-09.