86900110 ÷ 13 
Our goal is to divide 86900110 by 13.

Advancing to step 1:
When dividing 8 by 13, we get 0 with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 13

On to step 2:
13 goes into 86 6 times with a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 6.0
The remainder is 8 after subtracting 78 from 86.
Take the next digit (9) from the dividend and append it to 8, then repeat: 89 / 13

Let's proceed to step 3:
When dividing 89 by 13, we get 6 with a remainder of 11.
Write down 6 as next digit of the result. 
Result so far: 66.0
If we take 78 away from 89, we end up with 11.
Fetch the next digit (0) from the dividend, attach it to 11 and continue: 110 / 13

Going ahead to step 4:
110 divided by 13 is 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 668.0
Deduct 104 from 110 and we're left with 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 13

On to step 5:
13 goes into 60 4 times with a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 6684.0
The remainder is 8 after subtracting 52 from 60.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 13

On to step 6:
81 divided by 13 is 6 with a remainder of 3.
Write down 6 as next digit of the result. 
Result so far: 66846.0
Deduct 78 from 81 and we're left with 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 13

Going ahead to step 7:
If we divide 31 by 13, we get 2 and a remainder of 5.
Put 2 as the next digit of the answer. 
Result so far: 668462.0
If we subtract 26 from 31, we get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 13

Moving on to step 8:
13 goes into 50 3 times with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 6684623.0
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.

Advancing to step 9:
If we divide 110 by 13, we get 8 and a remainder of 6.
The next digit of our result is 8. 
Result so far: 6684623.8
Subtracting 104 from 110 leaves us 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.

Advancing to step 10:
13 goes into 60 4 times with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 6684623.84
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 11:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 6684623.846
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.

Moving on to step 12:
If we divide 20 by 13, we get 1 and a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 6684623.8461
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 13:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 6684623.84615
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.

Let's proceed to step 14:
50 divided by 13 is 3 with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 6684623.846153
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.

Going ahead to step 15:
When dividing 110 by 13, we get 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 6684623.8461538
Subtracting 104 from 110 leaves us 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.

Step 16:
13 goes into 60 4 times with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 6684623.84615384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

After the division, we end up with 6684623.84615384 and a remainder of 8e-09.