We're dividing 565476 by 13 
We want to figure out the number of times 565476 can be divided by 13.

On to step 1:
13 can be fit into 5 0 times, resulting in a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Grab the next digit (6) from the dividend, add it to 5, then carry on: 56 / 13

Advancing to step 2:
13 goes into 56 4 times with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 52 from 56 and we're left with 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 13

Step 3:
13 goes into 45 3 times with a remainder of 6.
Put 3 as the next digit of the answer. 
Result so far: 43.0
If we take 39 away from 45, we end up with 6.
Grab the next digit (4) from the dividend, add it to 6, then carry on: 64 / 13

Advancing to step 4:
If we divide 64 by 13, we get 4 and a remainder of 12.
Write down 4 as next digit of the result. 
Result so far: 434.0
If we subtract 52 from 64, we get 12.
Bring next digit (7) of the dividend behind the 12 and repeat the process: 127 / 13

Advancing to step 5:
13 can be fit into 127 9 times, resulting in a remainder of 10.
Record the quotient 9 as the next digit in the result. 
Result so far: 4349.0
Deduct 117 from 127 and we're left with 10.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 13

On to step 6:
When dividing 106 by 13, we get 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 43498.0
Subtracting 104 from 106 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 7:
When dividing 20 by 13, we get 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 43498.1
If we take 13 away from 20, we end up with 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 8:
13 can be fit into 70 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 43498.15
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 9:
If we divide 50 by 13, we get 3 and a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 43498.153
If we take 39 away from 50, we end up 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 10:
13 can be fit into 110 8 times, resulting in a remainder of 6.
The next digit of our result is 8. 
Result so far: 43498.1538
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.

Advancing to step 11:
When dividing 60 by 13, we get 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 43498.15384
The remainder is 8 after subtracting 52 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 12:
13 can be fit into 80 6 times, resulting in a remainder of 2.
The next digit of our result is 6. 
Result so far: 43498.153846
If we take 78 away from 80, we end up 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.

On to step 13:
If we divide 20 by 13, we get 1 and a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 43498.1538461
The remainder is 7 after subtracting 13 from 20.
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 14:
13 can be fit into 70 5 times, resulting in a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 43498.15384615
If we take 65 away from 70, we end up 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.

The final result is 43498.15384615 with a remainder of 5e-09.