We're dividing 565666 by 13 
We're looking to find how many times 13 goes into 565666.

Advancing to step 1:
5 divided by 13 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 13

Advancing to step 2:
56 divided by 13 is 4 with a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
The remainder is 4 after subtracting 52 from 56.
Take the next digit (5) from the dividend and append it to 4, then repeat: 45 / 13

On to step 3:
45 divided by 13 is 3 with a remainder of 6.
The next digit of our result is 3. 
Result so far: 43.0
Subtracting 39 from 45 leaves us with 6.
Take the next digit (6) from the dividend and append it to 6, then repeat: 66 / 13

Going ahead to step 4:
66 divided by 13 is 5 with a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 435.0
If we take 65 away from 66, we end up with 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 13

Going ahead to step 5:
13 goes into 16 1 times with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 4351.0
Subtracting 13 from 16 leaves us with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 13

Step 6:
13 can be fit into 36 2 times, resulting in a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 43512.0
The remainder is 10 after subtracting 26 from 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 7:
If we divide 100 by 13, we get 7 and a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 43512.7
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 8:
13 goes into 90 6 times with a remainder of 12.
The next digit of our result is 6. 
Result so far: 43512.76
Subtracting 78 from 90 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 9:
13 goes into 120 9 times with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 43512.769
If we take 117 away from 120, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 10:
When dividing 30 by 13, we get 2 with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 43512.7692
Deduct 26 from 30 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.

Step 11:
40 divided by 13 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 43512.76923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 12:
13 can be fit into 10 0 times, resulting in a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 43512.76923
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 13:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 43512.7692307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 14:
13 goes into 90 6 times with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 43512.76923076
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The quotient of the division is 43512.76923076, and the remainder is 1.2e-08.