605129 ÷ 13 
We're looking to find how many times 13 goes into 605129.

Step 1:
If we divide 6 by 13, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (0) from the dividend, attach it to 6 and continue: 60 / 13

Moving on to step 2:
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: 4.0
Subtracting 52 from 60 leaves us with 8.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 13

Advancing to step 3:
When dividing 85 by 13, we get 6 with a remainder of 7.
The next digit of our result is 6. 
Result so far: 46.0
Deduct 78 from 85 and we're left with 7.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 13

On to step 4:
If we divide 71 by 13, we get 5 and a remainder of 6.
Put 5 as the next digit of the answer. 
Result so far: 465.0
If we take 65 away from 71, we end up with 6.
Fetch the next digit (2) from the dividend, attach it to 6 and continue: 62 / 13

Going ahead to step 5:
62 divided by 13 is 4 with a remainder of 10.
Put 4 as the next digit of the answer. 
Result so far: 4654.0
Subtracting 52 from 62 leaves us with 10.
Bring next digit (9) of the dividend behind the 10 and repeat the process: 109 / 13

Let's proceed to step 6:
The number 13 fits into 109 8 times, leaving a remainder of 5.
Write down 8 as next digit of the result. 
Result so far: 46548.0
If we subtract 104 from 109, 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.

Let's proceed to step 7:
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: 46548.3
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.

Step 8:
The number 13 fits into 110 8 times, leaving a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 46548.38
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.

Let's proceed to step 9:
13 goes into 60 4 times with a remainder of 8.
The next digit of our result is 4. 
Result so far: 46548.384
Deduct 52 from 60 and we're left 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.

Going ahead to step 10:
13 goes into 80 6 times with a remainder of 2.
The next digit of our result is 6. 
Result so far: 46548.3846
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.

Step 11:
If we divide 20 by 13, we get 1 and a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 46548.38461
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.

Moving on to step 12:
The number 13 fits into 70 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 46548.384615
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.

On to step 13:
When dividing 50 by 13, we get 3 with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 46548.3846153
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.

Step 14:
13 goes into 110 8 times with a remainder of 6.
Write down 8 as next digit of the result. 
Result so far: 46548.38461538
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.

The quotient of the division is 46548.38461538, and the remainder is 6e-09.