We're dividing 79665 by 13 
We're looking to find how many times 13 goes into 79665.

Moving on to step 1:
The number 13 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Include the next digit (9) from the dividend after 7, then repeat: 79 / 13

Let's proceed to step 2:
If we divide 79 by 13, we get 6 and a remainder of 1.
The next digit of our result is 6. 
Result so far: 6.0
The remainder is 1 after subtracting 78 from 79.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 13

On to step 3:
If we divide 16 by 13, we get 1 and a remainder of 3.
The next digit of our result is 1. 
Result so far: 61.0
If we take 13 away from 16, we end up with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 13

Moving on to step 4:
If we divide 36 by 13, we get 2 and a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 612.0
Subtract 26 from 36 to get 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 13

Going ahead to step 5:
When dividing 105 by 13, we get 8 with a remainder of 1.
The next digit of our result is 8. 
Result so far: 6128.0
The remainder is 1 after subtracting 104 from 105.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 6:
If we divide 10 by 13, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 6128.0
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 7:
The number 13 fits into 100 7 times, leaving a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 6128.07
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 8:
If we divide 90 by 13, we get 6 and a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 6128.076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
If we divide 120 by 13, we get 9 and a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 6128.0769
If we take 117 away from 120, we end up 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.

Step 10:
30 divided by 13 is 2 with a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 6128.07692
If we take 26 away from 30, we end up 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.

Advancing to step 11:
When dividing 40 by 13, we get 3 with a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 6128.076923
If we take 39 away from 40, we end up with 1.
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 12:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 6128.076923
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.

Moving on to step 13:
100 divided by 13 is 7 with a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 6128.07692307
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

After the division, we end up with 6128.07692307 and a remainder of 9e-09.