We look at the division of 475643 by 13 
We want to divide 475643 by 13.

On to step 1:
The number 13 fits into 4 0 times, leaving a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 13

Step 2:
13 can be fit into 47 3 times, resulting in a remainder of 8.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtracting 39 from 47 leaves us with 8.
Bring next digit (5) of the dividend behind the 8 and repeat the process: 85 / 13

On to step 3:
When dividing 85 by 13, we get 6 with a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 36.0
Subtracting 78 from 85 leaves us with 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 13

Moving on to step 4:
13 goes into 76 5 times with a remainder of 11.
Record the quotient 5 as the next digit in the result. 
Result so far: 365.0
Subtract 65 from 76 to get 11.
Include the next digit (4) from the dividend after 11, then repeat: 114 / 13

Let's proceed to step 5:
13 goes into 114 8 times with a remainder of 10.
The next digit of our result is 8. 
Result so far: 3658.0
Subtract 104 from 114 to get 10.
Take the next digit (3) from the dividend and append it to 10, then repeat: 103 / 13

Advancing to step 6:
The number 13 fits into 103 7 times, leaving a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 36587.0
If we take 91 away from 103, we end up 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.

Step 7:
When dividing 120 by 13, we get 9 with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 36587.9
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 8:
If we divide 30 by 13, we get 2 and a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 36587.92
Subtract 26 from 30 to get 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 9:
When dividing 40 by 13, we get 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 36587.923
The remainder is 1 after subtracting 39 from 40.
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 10:
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: 36587.923
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 11:
13 can be fit into 100 7 times, resulting in a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 36587.92307
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.

Advancing to step 12:
90 divided by 13 is 6 with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 36587.923076
Deduct 78 from 90 and we're left 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.

On to step 13:
13 goes into 120 9 times with a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 36587.9230769
Subtract 117 from 120 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 14:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 36587.92307692
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.

After the division, we end up with 36587.92307692 and a remainder of 4e-09.