We look at the division of 14636 by 13 
Our goal is to divide 14636 by 13.

Going ahead to step 1:
If we divide 1 by 13, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (4) from the dividend to 1 and continue with: 14 / 13

Going ahead to step 2:
13 can be fit into 14 1 times, resulting in a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 13 from 14 and we're left with 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 13

Advancing to step 3:
The number 13 fits into 16 1 times, leaving a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
The remainder is 3 after subtracting 13 from 16.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 13

Advancing to step 4:
The number 13 fits into 33 2 times, leaving a remainder of 7.
Write down 2 as next digit of the result. 
Result so far: 112.0
If we take 26 away from 33, we end up with 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 13

Going ahead to step 5:
If we divide 76 by 13, we get 5 and a remainder of 11.
Record the quotient 5 as the next digit in the result. 
Result so far: 1125.0
If we take 65 away from 76, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 6:
If we divide 110 by 13, we get 8 and a remainder of 6.
Use 8 as the next digit of our solution. 
Result so far: 1125.8
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
13 goes into 60 4 times with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 1125.84
Subtract 52 from 60 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 8:
If we divide 80 by 13, we get 6 and a remainder of 2.
The next digit of our result is 6. 
Result so far: 1125.846
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 9:
13 goes into 20 1 times with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 1125.8461
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 10:
13 goes into 70 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 1125.84615
Subtracting 65 from 70 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 11:
13 goes into 50 3 times with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 1125.846153
Subtracting 39 from 50 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 12:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 1125.8461538
Subtract 104 from 110 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.

Going ahead to step 13:
If we divide 60 by 13, we get 4 and a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 1125.84615384
If we subtract 52 from 60, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 1125.84615384, and the remainder is 8e-09.