We look at the division of 976165 by 13 
We want to divide 976165 by 13.

Let's proceed to step 1:
9 divided by 13 is 0 with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Take the next digit (7) from the dividend and append it to 9, then repeat: 97 / 13

Moving on to step 2:
When dividing 97 by 13, we get 7 with a remainder of 6.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Deduct 91 from 97 and we're left with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 13

Advancing to step 3:
13 goes into 66 5 times with a remainder of 1.
Put 5 as the next digit of the answer. 
Result so far: 75.0
Subtract 65 from 66 to get 1.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 13

On to step 4:
11 divided by 13 is 0 with a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 750.0
If we subtract 0 from 11, we get 11.
Bring next digit (6) of the dividend behind the 11 and repeat the process: 116 / 13

Step 5:
If we divide 116 by 13, we get 8 and a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 7508.0
Deduct 104 from 116 and we're left with 12.
Fetch the next digit (5) from the dividend, attach it to 12 and continue: 125 / 13

Step 6:
13 can be fit into 125 9 times, resulting in a remainder of 8.
The next digit of our result is 9. 
Result so far: 75089.0
If we take 117 away from 125, we end up with 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 7:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 75089.6
If we take 78 away from 80, 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.

Let's proceed to step 8:
If we divide 20 by 13, we get 1 and a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 75089.61
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.

Going ahead to step 9:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 75089.615
The remainder is 5 after subtracting 65 from 70.
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 10:
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: 75089.6153
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.

Let's proceed to step 11:
The number 13 fits into 110 8 times, leaving a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 75089.61538
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 12:
When dividing 60 by 13, we get 4 with a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 75089.615384
Subtracting 52 from 60 leaves us with 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 13:
13 goes into 80 6 times with a remainder of 2.
The next digit of our result is 6. 
Result so far: 75089.6153846
Subtracting 78 from 80 leaves us 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.

Let's proceed to step 14:
13 goes into 20 1 times with a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 75089.61538461
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.

Our division results in 75089.61538461 with a remaining 7e-09.