We look at the division of 420741 by 4 
Let's see how many times 4 fits into 420741.

Moving on to step 1:
The number 4 fits into 4 1 times, leaving a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 4 from 4 and we're left with 0.
Fetch the next digit (2) from the dividend, attach it to 0 and continue: 2 / 4

Let's proceed to step 2:
4 goes into 2 0 times with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 2 after subtracting 0 from 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 4

Step 3:
The number 4 fits into 20 5 times, leaving a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 105.0
Subtract 20 from 20 to get 0.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 4

Moving on to step 4:
7 divided by 4 is 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 1051.0
Subtract 4 from 7 to get 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 4

Advancing to step 5:
4 goes into 34 8 times with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 10518.0
If we take 32 away from 34, we end up with 2.
Include the next digit (1) from the dividend after 2, then repeat: 21 / 4

Let's proceed to step 6:
4 can be fit into 21 5 times, resulting in a remainder of 1.
Write down 5 as next digit of the result. 
Result so far: 105185.0
Deduct 20 from 21 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 7:
When dividing 10 by 4, we get 2 with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 105185.2
The remainder is 2 after subtracting 8 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 8:
4 can be fit into 20 5 times, resulting in a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 105185.25
Subtracting 20 from 20 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 9:
When dividing 0 by 4, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 105185.25
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
The number 4 fits into 0 0 times, leaving a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 105185.25
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 105185.25 with a balance of 0.0.