561361 ÷ 9 
We're looking to find how many times 9 goes into 561361.

Step 1:
5 divided by 9 is 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (6) from the dividend to 5 and continue with: 56 / 9

On to step 2:
If we divide 56 by 9, we get 6 and a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtract 54 from 56 to get 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 9

Moving on to step 3:
9 can be fit into 21 2 times, resulting in a remainder of 3.
Put 2 as the next digit of the answer. 
Result so far: 62.0
The remainder is 3 after subtracting 18 from 21.
Include the next digit (3) from the dividend after 3, then repeat: 33 / 9

Advancing to step 4:
33 divided by 9 is 3 with a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 623.0
Subtracting 27 from 33 leaves us with 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 9

Let's proceed to step 5:
9 can be fit into 66 7 times, resulting in a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 6237.0
If we subtract 63 from 66, we get 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 9

Step 6:
31 divided by 9 is 3 with a remainder of 4.
Use 3 as the next digit of our solution. 
Result so far: 62373.0
If we take 27 away from 31, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
If we divide 40 by 9, we get 4 and a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 62373.4
If we take 36 away from 40, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 8:
40 divided by 9 is 4 with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 62373.44
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The final outcome is 62373.44, with a leftover of 0.004.