421854 ÷ 582 
Our goal is to divide 421854 by 582.

Moving on to step 1:
When dividing 4 by 582, we get 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 582

Advancing to step 2:
582 goes into 42 0 times with a remainder of 42.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 42 leaves us with 42.
Fetch the next digit (1) from the dividend, attach it to 42 and continue: 421 / 582

Moving on to step 3:
582 can be fit into 421 0 times, resulting in a remainder of 421.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 421 after subtracting 0 from 421.
Fetch the next digit (8) from the dividend, attach it to 421 and continue: 4218 / 582

Moving on to step 4:
4218 divided by 582 is 7 with a remainder of 144.
Write down 7 as next digit of the result. 
Result so far: 7.0
Deduct 4074 from 4218 and we're left with 144.
Take the next digit (5) from the dividend and append it to 144, then repeat: 1445 / 582

Going ahead to step 5:
1445 divided by 582 is 2 with a remainder of 281.
The number 2 becomes the next digit in our result. 
Result so far: 72.0
Subtract 1164 from 1445 to get 281.
Include the next digit (4) from the dividend after 281, then repeat: 2814 / 582

Going ahead to step 6:
582 goes into 2814 4 times with a remainder of 486.
The next digit of our result is 4. 
Result so far: 724.0
Subtracting 2328 from 2814 leaves us with 486.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4860, and continue the process.

Going ahead to step 7:
The number 582 fits into 4860 8 times, leaving a remainder of 204.
Record the quotient 8 as the next digit in the result. 
Result so far: 724.8
Subtract 4656 from 4860 to get 204.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2040, and continue the process.

Advancing to step 8:
582 goes into 2040 3 times with a remainder of 294.
Use 3 as the next digit of our solution. 
Result so far: 724.83
The remainder is 294 after subtracting 1746 from 2040.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2940, and continue the process.

Step 9:
If we divide 2940 by 582, we get 5 and a remainder of 30.
Put 5 as the next digit of the answer. 
Result so far: 724.835
Subtracting 2910 from 2940 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 10:
The number 582 fits into 300 0 times, leaving a remainder of 300.
Record the quotient 0 as the next digit in the result. 
Result so far: 724.835
Subtracting 0 from 300 leaves us with 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3000, and continue the process.

Going ahead to step 11:
When dividing 3000 by 582, we get 5 with a remainder of 90.
The number 5 becomes the next digit in our result. 
Result so far: 724.83505
If we subtract 2910 from 3000, we get 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Advancing to step 12:
The number 582 fits into 900 1 times, leaving a remainder of 318.
Put 1 as the next digit of the answer. 
Result so far: 724.835051
The remainder is 318 after subtracting 582 from 900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3180, and continue the process.

Going ahead to step 13:
582 goes into 3180 5 times with a remainder of 270.
Use 5 as the next digit of our solution. 
Result so far: 724.8350515
Subtracting 2910 from 3180 leaves us with 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2700, and continue the process.

Step 14:
If we divide 2700 by 582, we get 4 and a remainder of 372.
The number 4 becomes the next digit in our result. 
Result so far: 724.83505154
The remainder is 372 after subtracting 2328 from 2700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3720, and continue the process.

Our division results in 724.83505154 with a remaining 3.72e-07.