86376 ÷ 13 
Our goal is to divide 86376 by 13.

Advancing to step 1:
13 goes into 8 0 times with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Fetch the next digit (6) from the dividend, attach it to 8 and continue: 86 / 13

Advancing to step 2:
When dividing 86 by 13, we get 6 with a remainder of 8.
The next digit of our result is 6. 
Result so far: 6.0
If we subtract 78 from 86, we get 8.
Take the next digit (3) from the dividend and append it to 8, then repeat: 83 / 13

Step 3:
83 divided by 13 is 6 with a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 66.0
Deduct 78 from 83 and we're left with 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 13

Going ahead to step 4:
57 divided by 13 is 4 with a remainder of 5.
The number 4 becomes the next digit in our result. 
Result so far: 664.0
If we take 52 away from 57, we end up with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 13

Moving on to step 5:
When dividing 56 by 13, we get 4 with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 6644.0
Deduct 52 from 56 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 6:
40 divided by 13 is 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 6644.3
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 6644.3
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 8:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 6644.307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
90 divided by 13 is 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 6644.3076
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 10:
13 goes into 120 9 times with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 6644.30769
Subtracting 117 from 120 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.

Moving on to step 11:
When dividing 30 by 13, we get 2 with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 6644.307692
If we subtract 26 from 30, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 12:
If we divide 40 by 13, we get 3 and a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 6644.3076923
The remainder is 1 after subtracting 39 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 13:
The number 13 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 6644.3076923
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 6644.3076923 and a remainder of 1e-08.