We look at the division of 8408413 by 421 
Our goal is to divide 8408413 by 421.

Let's proceed to step 1:
421 can be fit into 8 0 times, resulting in a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Append the next digit (4) from the dividend to 8 and continue with: 84 / 421

Going ahead to step 2:
The number 421 fits into 84 0 times, leaving a remainder of 84.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 84, we end up with 84.
Take the next digit (0) from the dividend and append it to 84, then repeat: 840 / 421

Step 3:
421 goes into 840 1 times with a remainder of 419.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 421 from 840 leaves us with 419.
Take the next digit (8) from the dividend and append it to 419, then repeat: 4198 / 421

On to step 4:
When dividing 4198 by 421, we get 9 with a remainder of 409.
The number 9 becomes the next digit in our result. 
Result so far: 19.0
If we take 3789 away from 4198, we end up with 409.
Take the next digit (4) from the dividend and append it to 409, then repeat: 4094 / 421

Step 5:
The number 421 fits into 4094 9 times, leaving a remainder of 305.
Write down 9 as next digit of the result. 
Result so far: 199.0
The remainder is 305 after subtracting 3789 from 4094.
Grab the next digit (1) from the dividend, add it to 305, then carry on: 3051 / 421

On to step 6:
The number 421 fits into 3051 7 times, leaving a remainder of 104.
The next digit of our result is 7. 
Result so far: 1997.0
Deduct 2947 from 3051 and we're left with 104.
Grab the next digit (3) from the dividend, add it to 104, then carry on: 1043 / 421

Advancing to step 7:
421 goes into 1043 2 times with a remainder of 201.
Write down 2 as next digit of the result. 
Result so far: 19972.0
Deduct 842 from 1043 and we're left with 201.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2010, and continue the process.

Step 8:
The number 421 fits into 2010 4 times, leaving a remainder of 326.
Write down 4 as next digit of the result. 
Result so far: 19972.4
Deduct 1684 from 2010 and we're left with 326.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3260, and continue the process.

Advancing to step 9:
The number 421 fits into 3260 7 times, leaving a remainder of 313.
Use 7 as the next digit of our solution. 
Result so far: 19972.47
If we subtract 2947 from 3260, we get 313.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3130, and continue the process.

Moving on to step 10:
421 can be fit into 3130 7 times, resulting in a remainder of 183.
Use 7 as the next digit of our solution. 
Result so far: 19972.477
If we take 2947 away from 3130, we end up with 183.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1830, and continue the process.

The quotient of the division is 19972.477, and the remainder is 0.0183.