10681234 ÷ 513 
Let's see how many times 513 fits into 10681234.

Let's proceed to step 1:
513 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 513

On to step 2:
When dividing 10 by 513, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Take the next digit (6) from the dividend and append it to 10, then repeat: 106 / 513

Advancing to step 3:
513 goes into 106 0 times with a remainder of 106.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 106 after subtracting 0 from 106.
Fetch the next digit (8) from the dividend, attach it to 106 and continue: 1068 / 513

Advancing to step 4:
When dividing 1068 by 513, we get 2 with a remainder of 42.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
If we take 1026 away from 1068, we end up with 42.
Include the next digit (1) from the dividend after 42, then repeat: 421 / 513

On to step 5:
513 can be fit into 421 0 times, resulting in a remainder of 421.
Write down 0 as next digit of the result. 
Result so far: 20.0
Deduct 0 from 421 and we're left with 421.
Bring next digit (2) of the dividend behind the 421 and repeat the process: 4212 / 513

Moving on to step 6:
4212 divided by 513 is 8 with a remainder of 108.
The next digit of our result is 8. 
Result so far: 208.0
If we subtract 4104 from 4212, we get 108.
Bring next digit (3) of the dividend behind the 108 and repeat the process: 1083 / 513

On to step 7:
513 can be fit into 1083 2 times, resulting in a remainder of 57.
Put 2 as the next digit of the answer. 
Result so far: 2082.0
If we take 1026 away from 1083, we end up with 57.
Take the next digit (4) from the dividend and append it to 57, then repeat: 574 / 513

On to step 8:
If we divide 574 by 513, we get 1 and a remainder of 61.
Write down 1 as next digit of the result. 
Result so far: 20821.0
If we take 513 away from 574, we end up with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

On to step 9:
When dividing 610 by 513, we get 1 with a remainder of 97.
The number 1 becomes the next digit in our result. 
Result so far: 20821.1
If we subtract 513 from 610, we get 97.
Since there are no more digits in the dividend, we add a zero to the remainder making it 970, and continue the process.

On to step 10:
513 can be fit into 970 1 times, resulting in a remainder of 457.
The next digit of our result is 1. 
Result so far: 20821.11
The remainder is 457 after subtracting 513 from 970.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4570, and continue the process.

The quotient of the division is 20821.11, and the remainder is 0.457.