We look at the division of 422105 by 13 
We're looking to find how many times 13 goes into 422105.

Let's proceed to step 1:
13 goes into 4 0 times with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (2) from the dividend after 4, then repeat: 42 / 13

Step 2:
If we divide 42 by 13, we get 3 and a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 3.0
Subtract 39 from 42 to get 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 13

On to step 3:
13 goes into 32 2 times with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 32.0
Deduct 26 from 32 and we're left with 6.
Fetch the next digit (1) from the dividend, attach it to 6 and continue: 61 / 13

On to step 4:
If we divide 61 by 13, we get 4 and a remainder of 9.
Use 4 as the next digit of our solution. 
Result so far: 324.0
Deduct 52 from 61 and we're left with 9.
Grab the next digit (0) from the dividend, add it to 9, then carry on: 90 / 13

On to step 5:
When dividing 90 by 13, we get 6 with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 3246.0
The remainder is 12 after subtracting 78 from 90.
Append the next digit (5) from the dividend to 12 and continue with: 125 / 13

Let's proceed to step 6:
If we divide 125 by 13, we get 9 and a remainder of 8.
Put 9 as the next digit of the answer. 
Result so far: 32469.0
If we take 117 away from 125, 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.

Step 7:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 32469.6
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.

On to step 8:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The next digit of our result is 1. 
Result so far: 32469.61
Subtract 13 from 20 to 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.

Step 9:
The number 13 fits into 70 5 times, leaving a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 32469.615
Deduct 65 from 70 and we're left 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 10:
13 can be fit into 50 3 times, resulting in a remainder of 11.
The next digit of our result is 3. 
Result so far: 32469.6153
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.

Let's proceed to step 11:
13 goes into 110 8 times with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 32469.61538
If we subtract 104 from 110, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 12:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Write down 4 as next digit of the result. 
Result so far: 32469.615384
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.

On to step 13:
13 goes into 80 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 32469.6153846
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.

Moving on to step 14:
If we divide 20 by 13, we get 1 and a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 32469.61538461
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.

The final outcome is 32469.61538461, with a leftover of 7e-09.