We look at the division of 1412643 by 513 
We want to figure out the number of times 1412643 can be divided by 513.

Let's proceed to step 1:
The number 513 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 513

On to step 2:
14 divided by 513 is 0 with a remainder of 14.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 14 to get 14.
Fetch the next digit (1) from the dividend, attach it to 14 and continue: 141 / 513

Let's proceed to step 3:
When dividing 141 by 513, we get 0 with a remainder of 141.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 141, we end up with 141.
Bring next digit (2) of the dividend behind the 141 and repeat the process: 1412 / 513

Going ahead to step 4:
1412 divided by 513 is 2 with a remainder of 386.
The next digit of our result is 2. 
Result so far: 2.0
The remainder is 386 after subtracting 1026 from 1412.
Append the next digit (6) from the dividend to 386 and continue with: 3866 / 513

On to step 5:
When dividing 3866 by 513, we get 7 with a remainder of 275.
Use 7 as the next digit of our solution. 
Result so far: 27.0
Subtract 3591 from 3866 to get 275.
Grab the next digit (4) from the dividend, add it to 275, then carry on: 2754 / 513

Advancing to step 6:
The number 513 fits into 2754 5 times, leaving a remainder of 189.
Record the quotient 5 as the next digit in the result. 
Result so far: 275.0
Deduct 2565 from 2754 and we're left with 189.
Bring next digit (3) of the dividend behind the 189 and repeat the process: 1893 / 513

Let's proceed to step 7:
If we divide 1893 by 513, we get 3 and a remainder of 354.
Record the quotient 3 as the next digit in the result. 
Result so far: 2753.0
The remainder is 354 after subtracting 1539 from 1893.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3540, and continue the process.

Moving on to step 8:
If we divide 3540 by 513, we get 6 and a remainder of 462.
Record the quotient 6 as the next digit in the result. 
Result so far: 2753.6
If we take 3078 away from 3540, we end up with 462.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4620, and continue the process.

Going ahead to step 9:
The number 513 fits into 4620 9 times, leaving a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 2753.69
Deduct 4617 from 4620 and we're left 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.

Let's proceed to step 10:
513 goes into 30 0 times with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 2753.69
Subtracting 0 from 30 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 11:
300 divided by 513 is 0 with a remainder of 300.
Record the quotient 0 as the next digit in the result. 
Result so far: 2753.69
Subtract 0 from 300 to get 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3000, and continue the process.

The quotient of the division is 2753.69, and the remainder is 0.003.