6754 divided by 13 
We're looking to find how many times 13 goes into 6754.

Moving on to step 1:
If we divide 6 by 13, we get 0 and a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 13

Going ahead to step 2:
13 goes into 67 5 times with a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 65 away from 67, we end up with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 13

Going ahead to step 3:
The number 13 fits into 25 1 times, leaving a remainder of 12.
Write down 1 as next digit of the result. 
Result so far: 51.0
The remainder is 12 after subtracting 13 from 25.
Append the next digit (4) from the dividend to 12 and continue with: 124 / 13

On to step 4:
13 can be fit into 124 9 times, resulting in a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 519.0
If we take 117 away from 124, we end up 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 5:
13 can be fit into 70 5 times, resulting in a remainder of 5.
The next digit of our result is 5. 
Result so far: 519.5
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.

Let's proceed to step 6:
If we divide 50 by 13, we get 3 and a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 519.53
Deduct 39 from 50 and we're left 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:
The number 13 fits into 110 8 times, leaving a remainder of 6.
The next digit of our result is 8. 
Result so far: 519.538
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.

Moving on to step 8:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 519.5384
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.

Let's proceed to step 9:
When dividing 80 by 13, we get 6 with a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 519.53846
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.

Step 10:
If we divide 20 by 13, we get 1 and a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 519.538461
If we take 13 away from 20, we end up 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.

Moving on to step 11:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 519.5384615
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.

On to step 12:
When dividing 50 by 13, we get 3 with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 519.53846153
If we take 39 away from 50, 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.

The quotient of the division is 519.53846153, and the remainder is 1.1e-08.