168261 ÷ 13 
We're looking to find how many times 13 goes into 168261.

Step 1:
13 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 13

Advancing to step 2:
13 can be fit into 16 1 times, resulting in a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 13 from 16 and we're left with 3.
Fetch the next digit (8) from the dividend, attach it to 3 and continue: 38 / 13

Step 3:
38 divided by 13 is 2 with a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
If we subtract 26 from 38, we get 12.
Append the next digit (2) from the dividend to 12 and continue with: 122 / 13

Moving on to step 4:
When dividing 122 by 13, we get 9 with a remainder of 5.
Write down 9 as next digit of the result. 
Result so far: 129.0
Deduct 117 from 122 and we're left with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 13

On to step 5:
13 goes into 56 4 times with a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 1294.0
Subtract 52 from 56 to get 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 13

Moving on to step 6:
When dividing 41 by 13, we get 3 with a remainder of 2.
The next digit of our result is 3. 
Result so far: 12943.0
If we subtract 39 from 41, 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 7:
13 can be fit into 20 1 times, resulting in a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 12943.1
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 12943.15
If we take 65 away from 70, we end up 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.

Moving on to step 9:
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: 12943.153
Deduct 39 from 50 and we're left 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 10:
13 can be fit into 110 8 times, resulting in a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 12943.1538
The remainder is 6 after subtracting 104 from 110.
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 11:
13 can be fit into 60 4 times, resulting in a remainder of 8.
The next digit of our result is 4. 
Result so far: 12943.15384
If we take 52 away from 60, we end up 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.

Advancing to step 12:
13 can be fit into 80 6 times, resulting in a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 12943.153846
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.

Moving on to step 13:
The number 13 fits into 20 1 times, leaving a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 12943.1538461
If we subtract 13 from 20, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 14:
13 goes into 70 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 12943.15384615
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.

The quotient of the division is 12943.15384615, and the remainder is 5e-09.