We divide 262971 by 13
We're looking to find how many times 13 goes into 262971.

On to step 1:
When dividing 2 by 13, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 13

Moving on to step 2:
13 can be fit into 26 2 times, resulting in a remainder of 0.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
Subtracting 26 from 26 leaves us with 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 13

Moving on to step 3:
13 can be fit into 2 0 times, resulting in a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 20.0
Subtracting 0 from 2 leaves us with 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 13

On to step 4:
The number 13 fits into 29 2 times, leaving a remainder of 3.
The next digit of our result is 2. 
Result so far: 202.0
If we take 26 away from 29, we end up with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 13

Moving on to step 5:
37 divided by 13 is 2 with a remainder of 11.
The next digit of our result is 2. 
Result so far: 2022.0
Deduct 26 from 37 and we're left with 11.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 13

On to step 6:
When dividing 111 by 13, we get 8 with a remainder of 7.
The next digit of our result is 8. 
Result so far: 20228.0
Subtracting 104 from 111 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.

Step 7:
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: 20228.5
If we subtract 65 from 70, we 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.

Step 8:
When dividing 50 by 13, we get 3 with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 20228.53
The remainder is 11 after subtracting 39 from 50.
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 9:
If we divide 110 by 13, we get 8 and a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 20228.538
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.

On to step 10:
13 goes into 60 4 times with a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 20228.5384
If we subtract 52 from 60, we 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.

On to step 11:
80 divided by 13 is 6 with a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 20228.53846
The remainder is 2 after subtracting 78 from 80.
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 12:
When dividing 20 by 13, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 20228.538461
Deduct 13 from 20 and we're left 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.

Going ahead to step 13:
When dividing 70 by 13, we get 5 with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 20228.5384615
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.

Step 14:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 20228.53846153
Subtracting 39 from 50 leaves us 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.

Our division results in 20228.53846153 with a remaining 1.1e-08.