Let's divide 263666 by 233
We're looking to find how many times 233 goes into 263666.

Advancing to step 1:
If we divide 2 by 233, we get 0 and a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 233

On to step 2:
233 can be fit into 26 0 times, resulting in a remainder of 26.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 26 after subtracting 0 from 26.
Take the next digit (3) from the dividend and append it to 26, then repeat: 263 / 233

Let's proceed to step 3:
The number 233 fits into 263 1 times, leaving a remainder of 30.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 30 after subtracting 233 from 263.
Bring next digit (6) of the dividend behind the 30 and repeat the process: 306 / 233

Going ahead to step 4:
233 can be fit into 306 1 times, resulting in a remainder of 73.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we take 233 away from 306, we end up with 73.
Append the next digit (6) from the dividend to 73 and continue with: 736 / 233

Advancing to step 5:
The number 233 fits into 736 3 times, leaving a remainder of 37.
Record the quotient 3 as the next digit in the result. 
Result so far: 113.0
The remainder is 37 after subtracting 699 from 736.
Bring next digit (6) of the dividend behind the 37 and repeat the process: 376 / 233

Moving on to step 6:
The number 233 fits into 376 1 times, leaving a remainder of 143.
Use 1 as the next digit of our solution. 
Result so far: 1131.0
Subtracting 233 from 376 leaves us with 143.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1430, and continue the process.

Let's proceed to step 7:
When dividing 1430 by 233, we get 6 with a remainder of 32.
Use 6 as the next digit of our solution. 
Result so far: 1131.6
Deduct 1398 from 1430 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Going ahead to step 8:
320 divided by 233 is 1 with a remainder of 87.
Use 1 as the next digit of our solution. 
Result so far: 1131.61
The remainder is 87 after subtracting 233 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 870, and continue the process.

Advancing to step 9:
233 can be fit into 870 3 times, resulting in a remainder of 171.
Use 3 as the next digit of our solution. 
Result so far: 1131.613
Deduct 699 from 870 and we're left with 171.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1710, and continue the process.

Step 10:
1710 divided by 233 is 7 with a remainder of 79.
Use 7 as the next digit of our solution. 
Result so far: 1131.6137
Deduct 1631 from 1710 and we're left with 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

On to step 11:
233 can be fit into 790 3 times, resulting in a remainder of 91.
The next digit of our result is 3. 
Result so far: 1131.61373
Subtract 699 from 790 to get 91.
Since there are no more digits in the dividend, we add a zero to the remainder making it 910, and continue the process.

Let's proceed to step 12:
When dividing 910 by 233, we get 3 with a remainder of 211.
Put 3 as the next digit of the answer. 
Result so far: 1131.613733
Deduct 699 from 910 and we're left with 211.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2110, and continue the process.

The quotient of the division is 1131.613733, and the remainder is 2.11e-05.