We're dividing 2302 by 13 
We're looking to find how many times 13 goes into 2302.

Going ahead to step 1:
The number 13 fits into 2 0 times, leaving a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 13

Step 2:
If we divide 23 by 13, we get 1 and a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 13 from 23 to get 10.
Append the next digit (0) from the dividend to 10 and continue with: 100 / 13

On to step 3:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 17.0
Subtracting 91 from 100 leaves us with 9.
Bring next digit (2) of the dividend behind the 9 and repeat the process: 92 / 13

Advancing to step 4:
92 divided by 13 is 7 with a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 177.0
If we take 91 away from 92, 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.

Going ahead to step 5:
13 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 177.0
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 6:
If we divide 100 by 13, we get 7 and a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 177.07
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.

Let's proceed to step 7:
The number 13 fits into 90 6 times, leaving a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 177.076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 8:
120 divided by 13 is 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 177.0769
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.

Advancing to step 9:
The number 13 fits into 30 2 times, leaving a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 177.07692
Deduct 26 from 30 and we're left 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.

Going ahead to step 10:
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: 177.076923
Deduct 39 from 40 and we're left 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.

Moving on to step 11:
13 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 177.076923
Subtract 0 from 10 to 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.

Moving on to step 12:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 177.07692307
If we take 91 away from 100, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

The final result is 177.07692307 with a remainder of 9e-09.