13677 ÷ 17 
We're looking to find how many times 17 goes into 13677.

Moving on to step 1:
17 can be fit into 1 0 times, resulting in a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 17

Step 2:
When dividing 13 by 17, we get 0 with a remainder of 13.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 13 leaves us with 13.
Take the next digit (6) from the dividend and append it to 13, then repeat: 136 / 17

Let's proceed to step 3:
136 divided by 17 is 8 with a remainder of 0.
Use 8 as the next digit of our solution. 
Result so far: 8.0
The remainder is 0 after subtracting 136 from 136.
Append the next digit (7) from the dividend to 0 and continue with: 7 / 17

Let's proceed to step 4:
The number 17 fits into 7 0 times, leaving a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 80.0
If we take 0 away from 7, we end up with 7.
Take the next digit (7) from the dividend and append it to 7, then repeat: 77 / 17

On to step 5:
77 divided by 17 is 4 with a remainder of 9.
Write down 4 as next digit of the result. 
Result so far: 804.0
Deduct 68 from 77 and we're left 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.

Advancing to step 6:
If we divide 90 by 17, we get 5 and a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 804.5
Deduct 85 from 90 and we're left 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 7:
17 can be fit into 50 2 times, resulting in a remainder of 16.
The next digit of our result is 2. 
Result so far: 804.52
The remainder is 16 after subtracting 34 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 8:
17 can be fit into 160 9 times, resulting in a remainder of 7.
The next digit of our result is 9. 
Result so far: 804.529
Deduct 153 from 160 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 9:
17 can be fit into 70 4 times, resulting in a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 804.5294
If we take 68 away from 70, 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.

Step 10:
17 goes into 20 1 times with a remainder of 3.
The next digit of our result is 1. 
Result so far: 804.52941
Subtracting 17 from 20 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.

On to step 11:
The number 17 fits into 30 1 times, leaving a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 804.529411
Subtract 17 from 30 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 804.529411 with a balance of 1.3e-06.