We look at the division of 21669 by 23 
We want to figure out the number of times 21669 can be divided by 23.

Going ahead to step 1:
When dividing 2 by 23, we get 0 with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 23

On to step 2:
When dividing 21 by 23, we get 0 with a remainder of 21.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 21, we end up with 21.
Bring next digit (6) of the dividend behind the 21 and repeat the process: 216 / 23

Going ahead to step 3:
The number 23 fits into 216 9 times, leaving a remainder of 9.
Use 9 as the next digit of our solution. 
Result so far: 9.0
Deduct 207 from 216 and we're left with 9.
Fetch the next digit (6) from the dividend, attach it to 9 and continue: 96 / 23

On to step 4:
96 divided by 23 is 4 with a remainder of 4.
The next digit of our result is 4. 
Result so far: 94.0
Deduct 92 from 96 and we're left with 4.
Grab the next digit (9) from the dividend, add it to 4, then carry on: 49 / 23

Advancing to step 5:
23 goes into 49 2 times with a remainder of 3.
The next digit of our result is 2. 
Result so far: 942.0
The remainder is 3 after subtracting 46 from 49.
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 6:
When dividing 30 by 23, we get 1 with a remainder of 7.
The next digit of our result is 1. 
Result so far: 942.1
If we take 23 away from 30, we end up 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 7:
The number 23 fits into 70 3 times, leaving a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 942.13
If we subtract 69 from 70, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 8:
The number 23 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 942.13
Subtract 0 from 10 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 9:
23 goes into 100 4 times with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 942.1304
Subtracting 92 from 100 leaves us 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.

Going ahead to step 10:
When dividing 80 by 23, we get 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 942.13043
If we subtract 69 from 80, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 11:
23 can be fit into 110 4 times, resulting in a remainder of 18.
Record the quotient 4 as the next digit in the result. 
Result so far: 942.130434
Subtract 92 from 110 to 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.

Step 12:
23 can be fit into 180 7 times, resulting in a remainder of 19.
The next digit of our result is 7. 
Result so far: 942.1304347
Subtracting 161 from 180 leaves us with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 13:
If we divide 190 by 23, we get 8 and a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 942.13043478
The remainder is 6 after subtracting 184 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 942.13043478 and a remainder of 6e-09.