We're dividing 510603 by 23 
We want to figure out the number of times 510603 can be divided by 23.

Step 1:
23 can be fit into 5 0 times, resulting in a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 23

Step 2:
If we divide 51 by 23, we get 2 and a remainder of 5.
The next digit of our result is 2. 
Result so far: 2.0
If we subtract 46 from 51, we get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 23

Let's proceed to step 3:
The number 23 fits into 50 2 times, leaving a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 22.0
Subtract 46 from 50 to get 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 23

Let's proceed to step 4:
If we divide 46 by 23, we get 2 and a remainder of 0.
Put 2 as the next digit of the answer. 
Result so far: 222.0
The remainder is 0 after subtracting 46 from 46.
Include the next digit (0) from the dividend after 0, then repeat: 0 / 23

Going ahead to step 5:
0 divided by 23 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 2220.0
Deduct 0 from 0 and we're left with 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 23

Let's proceed to step 6:
If we divide 3 by 23, we get 0 and a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 22200.0
Deduct 0 from 3 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 7:
When dividing 30 by 23, we get 1 with a remainder of 7.
The next digit of our result is 1. 
Result so far: 22200.1
Subtract 23 from 30 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 8:
23 can be fit into 70 3 times, resulting in a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 22200.13
Subtracting 69 from 70 leaves us 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 9:
23 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 22200.13
If we take 0 away from 10, we end up 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 10:
100 divided by 23 is 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 22200.1304
If we take 92 away from 100, we end up 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 11:
When dividing 80 by 23, we get 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 22200.13043
Subtract 69 from 80 to 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.

Advancing to step 12:
When dividing 110 by 23, we get 4 with a remainder of 18.
Put 4 as the next digit of the answer. 
Result so far: 22200.130434
If we take 92 away from 110, 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.

Step 13:
23 goes into 180 7 times with a remainder of 19.
Put 7 as the next digit of the answer. 
Result so far: 22200.1304347
Deduct 161 from 180 and we're left 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 14:
When dividing 190 by 23, we get 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 22200.13043478
Subtract 184 from 190 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.

The final result is 22200.13043478 with a remainder of 6e-09.