510565 ÷ 61 
Let's see how many times 61 fits into 510565.

Step 1:
If we divide 5 by 61, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 61

Let's proceed to step 2:
51 divided by 61 is 0 with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 51, we get 51.
Include the next digit (0) from the dividend after 51, then repeat: 510 / 61

Advancing to step 3:
61 goes into 510 8 times with a remainder of 22.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
If we take 488 away from 510, we end up with 22.
Append the next digit (5) from the dividend to 22 and continue with: 225 / 61

Let's proceed to step 4:
61 can be fit into 225 3 times, resulting in a remainder of 42.
Use 3 as the next digit of our solution. 
Result so far: 83.0
If we take 183 away from 225, we end up with 42.
Bring next digit (6) of the dividend behind the 42 and repeat the process: 426 / 61

On to step 5:
61 can be fit into 426 6 times, resulting in a remainder of 60.
Write down 6 as next digit of the result. 
Result so far: 836.0
If we subtract 366 from 426, we get 60.
Fetch the next digit (5) from the dividend, attach it to 60 and continue: 605 / 61

Moving on to step 6:
61 can be fit into 605 9 times, resulting in a remainder of 56.
Use 9 as the next digit of our solution. 
Result so far: 8369.0
If we subtract 549 from 605, we get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Moving on to step 7:
The number 61 fits into 560 9 times, leaving a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 8369.9
If we subtract 549 from 560, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 8:
The number 61 fits into 110 1 times, leaving a remainder of 49.
Put 1 as the next digit of the answer. 
Result so far: 8369.91
The remainder is 49 after subtracting 61 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Going ahead to step 9:
490 divided by 61 is 8 with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 8369.918
The remainder is 2 after subtracting 488 from 490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 10:
61 goes into 20 0 times with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 8369.918
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 11:
The number 61 fits into 200 3 times, leaving a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 8369.91803
Subtract 183 from 200 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 12:
61 goes into 170 2 times with a remainder of 48.
Write down 2 as next digit of the result. 
Result so far: 8369.918032
If we subtract 122 from 170, we get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 13:
The number 61 fits into 480 7 times, leaving a remainder of 53.
Use 7 as the next digit of our solution. 
Result so far: 8369.9180327
If we take 427 away from 480, we end up with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Advancing to step 14:
When dividing 530 by 61, we get 8 with a remainder of 42.
Record the quotient 8 as the next digit in the result. 
Result so far: 8369.91803278
The remainder is 42 after subtracting 488 from 530.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

The final outcome is 8369.91803278, with a leftover of 4.2e-08.