561340 ÷ 13 
We're looking to find how many times 13 goes into 561340.

Step 1:
When dividing 5 by 13, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 13

On to step 2:
13 goes into 56 4 times with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 4.0
The remainder is 4 after subtracting 52 from 56.
Take the next digit (1) from the dividend and append it to 4, then repeat: 41 / 13

Advancing to step 3:
When dividing 41 by 13, we get 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 43.0
Deduct 39 from 41 and we're left with 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 13

Step 4:
The number 13 fits into 23 1 times, leaving a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 431.0
Subtract 13 from 23 to get 10.
Grab the next digit (4) from the dividend, add it to 10, then carry on: 104 / 13

Moving on to step 5:
13 can be fit into 104 8 times, resulting in a remainder of 0.
The number 8 becomes the next digit in our result. 
Result so far: 4318.0
If we take 104 away from 104, we end up with 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 13

On to step 6:
The number 13 fits into 0 0 times, leaving a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 43180.0
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 7:
13 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 43180.0
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 8:
If we divide 0 by 13, we get 0 and a remainder of 0.
The next digit of our result is 0. 
Result so far: 43180.0
If we take 0 away from 0, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 43180.0 with a balance of 0.0.