We're dividing 181903 by 21 
We're looking to find how many times 21 goes into 181903.

Step 1:
When dividing 1 by 21, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 21

Step 2:
If we divide 18 by 21, we get 0 and a remainder of 18.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 18 after subtracting 0 from 18.
Fetch the next digit (1) from the dividend, attach it to 18 and continue: 181 / 21

On to step 3:
The number 21 fits into 181 8 times, leaving a remainder of 13.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we subtract 168 from 181, we get 13.
Take the next digit (9) from the dividend and append it to 13, then repeat: 139 / 21

On to step 4:
21 can be fit into 139 6 times, resulting in a remainder of 13.
Put 6 as the next digit of the answer. 
Result so far: 86.0
Subtracting 126 from 139 leaves us with 13.
Append the next digit (0) from the dividend to 13 and continue with: 130 / 21

Advancing to step 5:
21 goes into 130 6 times with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 866.0
Subtract 126 from 130 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 21

Let's proceed to step 6:
When dividing 43 by 21, we get 2 with a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 8662.0
If we take 42 away from 43, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
21 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 8662.0
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
If we divide 100 by 21, we get 4 and a remainder of 16.
The next digit of our result is 4. 
Result so far: 8662.04
Deduct 84 from 100 and we're left 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.

Going ahead to step 9:
21 can be fit into 160 7 times, resulting in a remainder of 13.
Put 7 as the next digit of the answer. 
Result so far: 8662.047
Subtracting 147 from 160 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 10:
21 goes into 130 6 times with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 8662.0476
Deduct 126 from 130 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 11:
40 divided by 21 is 1 with a remainder of 19.
The number 1 becomes the next digit in our result. 
Result so far: 8662.04761
The remainder is 19 after subtracting 21 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 12:
21 can be fit into 190 9 times, resulting in a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 8662.047619
If we take 189 away from 190, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 13:
21 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 8662.047619
Subtracting 0 from 10 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.

Moving on to step 14:
21 can be fit into 100 4 times, resulting in a remainder of 16.
Use 4 as the next digit of our solution. 
Result so far: 8662.04761904
Subtract 84 from 100 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

After the division, we end up with 8662.04761904 and a remainder of 1.6e-08.