We look at the division of 42070414 by 513 
We want to divide 42070414 by 513.

On to step 1:
The number 513 fits into 4 0 times, leaving a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 513

Advancing to step 2:
42 divided by 513 is 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 42, we end up with 42.
Fetch the next digit (0) from the dividend, attach it to 42 and continue: 420 / 513

Step 3:
513 goes into 420 0 times with a remainder of 420.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 420 to get 420.
Take the next digit (7) from the dividend and append it to 420, then repeat: 4207 / 513

Let's proceed to step 4:
If we divide 4207 by 513, we get 8 and a remainder of 103.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we take 4104 away from 4207, we end up with 103.
Append the next digit (0) from the dividend to 103 and continue with: 1030 / 513

Advancing to step 5:
513 goes into 1030 2 times with a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 82.0
If we subtract 1026 from 1030, we get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 513

Step 6:
44 divided by 513 is 0 with a remainder of 44.
The number 0 becomes the next digit in our result. 
Result so far: 820.0
The remainder is 44 after subtracting 0 from 44.
Take the next digit (1) from the dividend and append it to 44, then repeat: 441 / 513

Moving on to step 7:
441 divided by 513 is 0 with a remainder of 441.
Use 0 as the next digit of our solution. 
Result so far: 8200.0
The remainder is 441 after subtracting 0 from 441.
Include the next digit (4) from the dividend after 441, then repeat: 4414 / 513

Step 8:
When dividing 4414 by 513, we get 8 with a remainder of 310.
The number 8 becomes the next digit in our result. 
Result so far: 82008.0
Deduct 4104 from 4414 and we're left with 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3100, and continue the process.

Let's proceed to step 9:
When dividing 3100 by 513, we get 6 with a remainder of 22.
The next digit of our result is 6. 
Result so far: 82008.6
Deduct 3078 from 3100 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 10:
513 can be fit into 220 0 times, resulting in a remainder of 220.
The next digit of our result is 0. 
Result so far: 82008.6
Subtracting 0 from 220 leaves us with 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2200, and continue the process.

On to step 11:
2200 divided by 513 is 4 with a remainder of 148.
Put 4 as the next digit of the answer. 
Result so far: 82008.604
Subtracting 2052 from 2200 leaves us with 148.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1480, and continue the process.

Let's proceed to step 12:
513 can be fit into 1480 2 times, resulting in a remainder of 454.
The next digit of our result is 2. 
Result so far: 82008.6042
Deduct 1026 from 1480 and we're left with 454.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4540, and continue the process.

Advancing to step 13:
513 goes into 4540 8 times with a remainder of 436.
The next digit of our result is 8. 
Result so far: 82008.60428
Subtract 4104 from 4540 to get 436.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4360, and continue the process.

Moving on to step 14:
The number 513 fits into 4360 8 times, leaving a remainder of 256.
Put 8 as the next digit of the answer. 
Result so far: 82008.604288
Subtracting 4104 from 4360 leaves us with 256.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2560, and continue the process.

The final result is 82008.604288 with a remainder of 2.56e-05.