108743 ÷ 13 
Let's see how many times 13 fits into 108743.

On to step 1:
13 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

Advancing to step 2:
If we divide 10 by 13, we get 0 and a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (8) from the dividend, attach it to 10 and continue: 108 / 13

Advancing to step 3:
13 can be fit into 108 8 times, resulting in a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 8.0
The remainder is 4 after subtracting 104 from 108.
Fetch the next digit (7) from the dividend, attach it to 4 and continue: 47 / 13

Step 4:
When dividing 47 by 13, we get 3 with a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 83.0
Subtracting 39 from 47 leaves us with 8.
Append the next digit (4) from the dividend to 8 and continue with: 84 / 13

Advancing to step 5:
If we divide 84 by 13, we get 6 and a remainder of 6.
The next digit of our result is 6. 
Result so far: 836.0
If we subtract 78 from 84, we get 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 13

On to step 6:
When dividing 63 by 13, we get 4 with a remainder of 11.
The number 4 becomes the next digit in our result. 
Result so far: 8364.0
Subtracting 52 from 63 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.

Step 7:
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: 8364.8
If we subtract 104 from 110, we 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 8:
13 can be fit into 60 4 times, resulting in a remainder of 8.
The next digit of our result is 4. 
Result so far: 8364.84
If we take 52 away from 60, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
13 goes into 80 6 times with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 8364.846
Deduct 78 from 80 and we're left 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 10:
20 divided by 13 is 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 8364.8461
Subtracting 13 from 20 leaves us 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.

Let's proceed to step 11:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 8364.84615
Subtract 65 from 70 to get 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 12:
50 divided by 13 is 3 with a remainder of 11.
The next digit of our result is 3. 
Result so far: 8364.846153
If we subtract 39 from 50, we 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.

Advancing to step 13:
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: 8364.8461538
If we take 104 away from 110, we end up with 6.
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 14:
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: 8364.84615384
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 8364.84615384, and the remainder is 8e-09.