Let's divide 12669 by 21
We want to figure out the number of times 12669 can be divided by 21.

Going ahead to step 1:
21 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of 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

On to step 2:
21 goes into 12 0 times with a remainder of 12.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 12 and we're left with 12.
Take the next digit (6) from the dividend and append it to 12, then repeat: 126 / 21

Step 3:
The number 21 fits into 126 6 times, leaving a remainder of 0.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtract 126 from 126 to get 0.
Take the next digit (6) from the dividend and append it to 0, then repeat: 6 / 21

Let's proceed to step 4:
21 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 60.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (9) from the dividend, attach it to 6 and continue: 69 / 21

Advancing to step 5:
When dividing 69 by 21, we get 3 with a remainder of 6.
The number 3 becomes the next digit in our result. 
Result so far: 603.0
Deduct 63 from 69 and we're left 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.

Going ahead to step 6:
21 goes into 60 2 times with a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 603.2
Deduct 42 from 60 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 7:
If we divide 180 by 21, we get 8 and a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 603.28
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.

Moving on to step 8:
21 can be fit into 120 5 times, resulting in a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 603.285
The remainder is 15 after subtracting 105 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 9:
21 can be fit into 150 7 times, resulting in a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 603.2857
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.

Moving on to step 10:
21 can be fit into 30 1 times, resulting in a remainder of 9.
The next digit of our result is 1. 
Result so far: 603.28571
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.

Going ahead to step 11:
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: 603.285714
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.

Advancing to step 12:
If we divide 60 by 21, we get 2 and a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 603.2857142
If we take 42 away from 60, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 13:
When dividing 180 by 21, we get 8 with a remainder of 12.
The next digit of our result is 8. 
Result so far: 603.28571428
Subtracting 168 from 180 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.

The final outcome is 603.28571428, with a leftover of 1.2e-08.