We're dividing 965830 by 13 
We're looking to find how many times 13 goes into 965830.

Let's proceed to step 1:
13 can be fit into 9 0 times, resulting in a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 9, we end up with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 13

Going ahead to step 2:
If we divide 96 by 13, we get 7 and a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we take 91 away from 96, we end up with 5.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 13

Let's proceed to step 3:
55 divided by 13 is 4 with a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 74.0
If we subtract 52 from 55, we get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 13

Moving on to step 4:
13 can be fit into 38 2 times, resulting in a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 742.0
If we take 26 away from 38, we end up with 12.
Append the next digit (3) from the dividend to 12 and continue with: 123 / 13

On to step 5:
13 can be fit into 123 9 times, resulting in a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 7429.0
Deduct 117 from 123 and we're left with 6.
Include the next digit (0) from the dividend after 6, then repeat: 60 / 13

Let's proceed to step 6:
60 divided by 13 is 4 with a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 74294.0
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.

Let's proceed to step 7:
13 can be fit into 80 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 74294.6
Subtract 78 from 80 to 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.

Advancing to step 8:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Put 1 as the next digit of the answer. 
Result so far: 74294.61
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.

Advancing to step 9:
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: 74294.615
Subtracting 65 from 70 leaves us 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.

Going ahead to step 10:
The number 13 fits into 50 3 times, leaving a remainder of 11.
The number 3 becomes the next digit in our result. 
Result so far: 74294.6153
If we take 39 away from 50, we end up 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.

On to step 11:
When dividing 110 by 13, we get 8 with a remainder of 6.
The next digit of our result is 8. 
Result so far: 74294.61538
If we take 104 away from 110, we end up 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.

Going ahead to step 12:
60 divided by 13 is 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 74294.615384
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.

Moving on to step 13:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 74294.6153846
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.

Let's proceed to step 14:
20 divided by 13 is 1 with a remainder of 7.
The next digit of our result is 1. 
Result so far: 74294.61538461
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.

In conclusion, the division gives 74294.61538461 with a balance of 7e-09.