413819 divided by 684 
We want to divide 413819 by 684.

Step 1:
If we divide 4 by 684, we get 0 and a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 684

Step 2:
41 divided by 684 is 0 with a remainder of 41.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 41 after subtracting 0 from 41.
Grab the next digit (3) from the dividend, add it to 41, then carry on: 413 / 684

Moving on to step 3:
When dividing 413 by 684, we get 0 with a remainder of 413.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 413 after subtracting 0 from 413.
Bring next digit (8) of the dividend behind the 413 and repeat the process: 4138 / 684

On to step 4:
4138 divided by 684 is 6 with a remainder of 34.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
The remainder is 34 after subtracting 4104 from 4138.
Fetch the next digit (1) from the dividend, attach it to 34 and continue: 341 / 684

On to step 5:
341 divided by 684 is 0 with a remainder of 341.
Use 0 as the next digit of our solution. 
Result so far: 60.0
Deduct 0 from 341 and we're left with 341.
Fetch the next digit (9) from the dividend, attach it to 341 and continue: 3419 / 684

Going ahead to step 6:
When dividing 3419 by 684, we get 4 with a remainder of 683.
Put 4 as the next digit of the answer. 
Result so far: 604.0
Subtracting 2736 from 3419 leaves us with 683.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6830, and continue the process.

On to step 7:
684 can be fit into 6830 9 times, resulting in a remainder of 674.
The number 9 becomes the next digit in our result. 
Result so far: 604.9
Subtract 6156 from 6830 to get 674.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6740, and continue the process.

On to step 8:
If we divide 6740 by 684, we get 9 and a remainder of 584.
The number 9 becomes the next digit in our result. 
Result so far: 604.99
Subtracting 6156 from 6740 leaves us with 584.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5840, and continue the process.

The quotient of the division is 604.99, and the remainder is 0.584.