Let's divide 35663 by 13
Our goal is to divide 35663 by 13.

Advancing to step 1:
13 can be fit into 3 0 times, resulting in a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 13

On to step 2:
The number 13 fits into 35 2 times, leaving a remainder of 9.
Use 2 as the next digit of our solution. 
Result so far: 2.0
The remainder is 9 after subtracting 26 from 35.
Bring next digit (6) of the dividend behind the 9 and repeat the process: 96 / 13

Going ahead to step 3:
When dividing 96 by 13, we get 7 with a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 27.0
The remainder is 5 after subtracting 91 from 96.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 13

Moving on to step 4:
13 goes into 56 4 times with a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 274.0
Subtracting 52 from 56 leaves us with 4.
Fetch the next digit (3) from the dividend, attach it to 4 and continue: 43 / 13

Advancing to step 5:
If we divide 43 by 13, we get 3 and a remainder of 4.
The number 3 becomes the next digit in our result. 
Result so far: 2743.0
Deduct 39 from 43 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.

Moving on to step 6:
If we divide 40 by 13, we get 3 and a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 2743.3
Deduct 39 from 40 and we're left 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.

Step 7:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 2743.3
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.

Advancing to step 8:
13 goes into 100 7 times with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 2743.307
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 2743.3076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 10:
If we divide 120 by 13, we get 9 and a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 2743.30769
Subtracting 117 from 120 leaves us 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.

Going ahead to step 11:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 2743.307692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 12:
If we divide 40 by 13, we get 3 and a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 2743.3076923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 13:
13 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 2743.3076923
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.

The quotient of the division is 2743.3076923, and the remainder is 1e-08.