We look at the division of 107465 by 13 
We want to divide 107465 by 13.

On to step 1:
1 divided by 13 is 0 with 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.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 13

Advancing to step 2:
10 divided by 13 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Bring next digit (7) of the dividend behind the 10 and repeat the process: 107 / 13

Moving on to step 3:
The number 13 fits into 107 8 times, leaving a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 8.0
If we subtract 104 from 107, we get 3.
Grab the next digit (4) from the dividend, add it to 3, then carry on: 34 / 13

Step 4:
If we divide 34 by 13, we get 2 and a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 82.0
Deduct 26 from 34 and we're left with 8.
Include the next digit (6) from the dividend after 8, then repeat: 86 / 13

On to step 5:
If we divide 86 by 13, we get 6 and a remainder of 8.
Use 6 as the next digit of our solution. 
Result so far: 826.0
The remainder is 8 after subtracting 78 from 86.
Bring next digit (5) of the dividend behind the 8 and repeat the process: 85 / 13

Step 6:
When dividing 85 by 13, we get 6 with a remainder of 7.
The next digit of our result is 6. 
Result so far: 8266.0
If we take 78 away from 85, 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.

Going ahead to step 7:
13 can be fit into 70 5 times, resulting in a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 8266.5
Deduct 65 from 70 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 8:
50 divided by 13 is 3 with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 8266.53
Subtract 39 from 50 to 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.

Step 9:
110 divided by 13 is 8 with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 8266.538
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.

Going ahead to step 10:
13 can be fit into 60 4 times, resulting in a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 8266.5384
Subtract 52 from 60 to 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.

Step 11:
13 goes into 80 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 8266.53846
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 12:
20 divided by 13 is 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 8266.538461
Subtract 13 from 20 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 13:
If we divide 70 by 13, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 8266.5384615
If we subtract 65 from 70, we 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.

Advancing to step 14:
13 goes into 50 3 times with a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 8266.53846153
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.

The final result is 8266.53846153 with a remainder of 1.1e-08.