We're dividing 513945 by 41 
Our goal is to divide 513945 by 41.

Let's proceed to step 1:
The number 41 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 41

Moving on to step 2:
When dividing 51 by 41, we get 1 with a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 41 from 51, we get 10.
Append the next digit (3) from the dividend to 10 and continue with: 103 / 41

Moving on to step 3:
41 can be fit into 103 2 times, resulting in a remainder of 21.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
Deduct 82 from 103 and we're left with 21.
Append the next digit (9) from the dividend to 21 and continue with: 219 / 41

On to step 4:
41 goes into 219 5 times with a remainder of 14.
Use 5 as the next digit of our solution. 
Result so far: 125.0
If we take 205 away from 219, we end up with 14.
Take the next digit (4) from the dividend and append it to 14, then repeat: 144 / 41

Advancing to step 5:
41 can be fit into 144 3 times, resulting in a remainder of 21.
Record the quotient 3 as the next digit in the result. 
Result so far: 1253.0
If we take 123 away from 144, we end up with 21.
Include the next digit (5) from the dividend after 21, then repeat: 215 / 41

Let's proceed to step 6:
41 goes into 215 5 times with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 12535.0
Subtracting 205 from 215 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.

Let's proceed to step 7:
If we divide 100 by 41, we get 2 and a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 12535.2
The remainder is 18 after subtracting 82 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 8:
41 can be fit into 180 4 times, resulting in a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 12535.24
If we take 164 away from 180, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 9:
160 divided by 41 is 3 with a remainder of 37.
Use 3 as the next digit of our solution. 
Result so far: 12535.243
Subtract 123 from 160 to get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Going ahead to step 10:
If we divide 370 by 41, we get 9 and a remainder of 1.
Write down 9 as next digit of the result. 
Result so far: 12535.2439
If we subtract 369 from 370, 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.

Step 11:
If we divide 10 by 41, we get 0 and a remainder of 10.
The next digit of our result is 0. 
Result so far: 12535.2439
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.

Moving on to step 12:
41 can be fit into 100 2 times, resulting in a remainder of 18.
The number 2 becomes the next digit in our result. 
Result so far: 12535.243902
The remainder is 18 after subtracting 82 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Moving on to step 13:
If we divide 180 by 41, we get 4 and a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 12535.2439024
Deduct 164 from 180 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 14:
When dividing 160 by 41, we get 3 with a remainder of 37.
The next digit of our result is 3. 
Result so far: 12535.24390243
Subtracting 123 from 160 leaves us with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

The quotient of the division is 12535.24390243, and the remainder is 3.7e-08.