We divide 523633 by 2
We're looking to find how many times 2 goes into 523633.

Advancing to step 1:
5 divided by 2 is 2 with a remainder of 1.
The next digit of our result is 2. 
Result so far: 2.0
Subtracting 4 from 5 leaves us with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 2

Advancing to step 2:
When dividing 12 by 2, we get 6 with a remainder of 0.
Record the quotient 6 as the next digit in the result. 
Result so far: 26.0
If we subtract 12 from 12, we get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 2

Moving on to step 3:
If we divide 3 by 2, we get 1 and a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 261.0
The remainder is 1 after subtracting 2 from 3.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 2

Let's proceed to step 4:
2 goes into 16 8 times with a remainder of 0.
Write down 8 as next digit of the result. 
Result so far: 2618.0
Subtract 16 from 16 to get 0.
Fetch the next digit (3) from the dividend, attach it to 0 and continue: 3 / 2

On to step 5:
When dividing 3 by 2, we get 1 with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 26181.0
If we take 2 away from 3, we end up with 1.
Take the next digit (3) from the dividend and append it to 1, then repeat: 13 / 2

Step 6:
2 can be fit into 13 6 times, resulting in a remainder of 1.
Put 6 as the next digit of the answer. 
Result so far: 261816.0
If we take 12 away from 13, 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.

On to step 7:
2 goes into 10 5 times with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 261816.5
If we take 10 away from 10, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
2 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 261816.5
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 9:
2 can be fit into 0 0 times, resulting in a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 261816.5
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 261816.5, and the remainder is 0.0.