Let's divide 1725913 by 421
Our goal is to divide 1725913 by 421.

Step 1:
When dividing 1 by 421, we get 0 with 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.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 421

On to step 2:
If we divide 17 by 421, we get 0 and a remainder of 17.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Append the next digit (2) from the dividend to 17 and continue with: 172 / 421

Advancing to step 3:
If we divide 172 by 421, we get 0 and a remainder of 172.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 172, we get 172.
Include the next digit (5) from the dividend after 172, then repeat: 1725 / 421

Let's proceed to step 4:
When dividing 1725 by 421, we get 4 with a remainder of 41.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 1684 away from 1725, we end up with 41.
Include the next digit (9) from the dividend after 41, then repeat: 419 / 421

Let's proceed to step 5:
421 goes into 419 0 times with a remainder of 419.
Record the quotient 0 as the next digit in the result. 
Result so far: 40.0
If we subtract 0 from 419, we get 419.
Bring next digit (1) of the dividend behind the 419 and repeat the process: 4191 / 421

Let's proceed to step 6:
If we divide 4191 by 421, we get 9 and a remainder of 402.
The next digit of our result is 9. 
Result so far: 409.0
The remainder is 402 after subtracting 3789 from 4191.
Take the next digit (3) from the dividend and append it to 402, then repeat: 4023 / 421

Moving on to step 7:
When dividing 4023 by 421, we get 9 with a remainder of 234.
Put 9 as the next digit of the answer. 
Result so far: 4099.0
Subtracting 3789 from 4023 leaves us with 234.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2340, and continue the process.

Advancing to step 8:
421 can be fit into 2340 5 times, resulting in a remainder of 235.
Write down 5 as next digit of the result. 
Result so far: 4099.5
Subtracting 2105 from 2340 leaves us with 235.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2350, and continue the process.

Advancing to step 9:
421 can be fit into 2350 5 times, resulting in a remainder of 245.
Record the quotient 5 as the next digit in the result. 
Result so far: 4099.55
Deduct 2105 from 2350 and we're left with 245.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2450, and continue the process.

Our division results in 4099.55 with a remaining 0.245.