111636 ÷ 13 
We want to figure out the number of times 111636 can be divided by 13.

Step 1:
13 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 13

Advancing to step 2:
If we divide 11 by 13, we get 0 and a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 11, we get 11.
Fetch the next digit (1) from the dividend, attach it to 11 and continue: 111 / 13

Step 3:
If we divide 111 by 13, we get 8 and a remainder of 7.
Write down 8 as next digit of the result. 
Result so far: 8.0
Deduct 104 from 111 and we're left with 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 13

Moving on to step 4:
13 goes into 76 5 times with a remainder of 11.
The next digit of our result is 5. 
Result so far: 85.0
If we take 65 away from 76, we end up with 11.
Include the next digit (3) from the dividend after 11, then repeat: 113 / 13

On to step 5:
When dividing 113 by 13, we get 8 with a remainder of 9.
Use 8 as the next digit of our solution. 
Result so far: 858.0
The remainder is 9 after subtracting 104 from 113.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 13

Step 6:
13 can be fit into 96 7 times, resulting in a remainder of 5.
Put 7 as the next digit of the answer. 
Result so far: 8587.0
Subtracting 91 from 96 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.

Step 7:
When dividing 50 by 13, we get 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 8587.3
The remainder is 11 after subtracting 39 from 50.
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 8:
When dividing 110 by 13, we get 8 with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 8587.38
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.

Advancing to step 9:
When dividing 60 by 13, we get 4 with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 8587.384
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.

Let's proceed to step 10:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 8587.3846
If we take 78 away from 80, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 11:
20 divided by 13 is 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 8587.38461
Deduct 13 from 20 and we're left with 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 12:
13 goes into 70 5 times with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 8587.384615
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.

Let's proceed to step 13:
50 divided by 13 is 3 with a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 8587.3846153
Subtract 39 from 50 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.

Moving on to step 14:
110 divided by 13 is 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 8587.38461538
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.

The quotient of the division is 8587.38461538, and the remainder is 6e-09.