765006 ÷ 13 
Our goal is to divide 765006 by 13.

On to step 1:
13 can be fit into 7 0 times, resulting in a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 13

Advancing to step 2:
The number 13 fits into 76 5 times, leaving a remainder of 11.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 65 from 76 leaves us with 11.
Include the next digit (5) from the dividend after 11, then repeat: 115 / 13

Let's proceed to step 3:
13 can be fit into 115 8 times, resulting in a remainder of 11.
The number 8 becomes the next digit in our result. 
Result so far: 58.0
Subtracting 104 from 115 leaves us with 11.
Take the next digit (0) from the dividend and append it to 11, then repeat: 110 / 13

Advancing to step 4:
The number 13 fits into 110 8 times, leaving a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 588.0
Deduct 104 from 110 and we're left with 6.
Grab the next digit (0) from the dividend, add it to 6, then carry on: 60 / 13

Going ahead 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: 5884.0
If we take 52 away from 60, we end up with 8.
Take the next digit (6) from the dividend and append it to 8, then repeat: 86 / 13

Step 6:
13 goes into 86 6 times with a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 58846.0
Subtract 78 from 86 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.

Let's proceed to step 7:
If we divide 80 by 13, we get 6 and a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 58846.6
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 8:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 58846.61
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:
When dividing 70 by 13, we get 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 58846.615
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.

Moving on to step 10:
If we divide 50 by 13, we get 3 and a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 58846.6153
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.

Let's proceed to step 11:
13 can be fit into 110 8 times, resulting in a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 58846.61538
Deduct 104 from 110 and we're left 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.

Let's proceed to step 12:
When dividing 60 by 13, we get 4 with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 58846.615384
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.

Going ahead to step 13:
80 divided by 13 is 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 58846.6153846
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:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 58846.61538461
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 58846.61538461 with a balance of 7e-09.