306421 ÷ 53 
Our goal is to divide 306421 by 53.

Going ahead to step 1:
If we divide 3 by 53, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Include the next digit (0) from the dividend after 3, then repeat: 30 / 53

On to step 2:
If we divide 30 by 53, we get 0 and a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 30 leaves us with 30.
Take the next digit (6) from the dividend and append it to 30, then repeat: 306 / 53

Going ahead to step 3:
306 divided by 53 is 5 with a remainder of 41.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
Subtract 265 from 306 to get 41.
Take the next digit (4) from the dividend and append it to 41, then repeat: 414 / 53

On to step 4:
53 can be fit into 414 7 times, resulting in a remainder of 43.
Record the quotient 7 as the next digit in the result. 
Result so far: 57.0
Deduct 371 from 414 and we're left with 43.
Take the next digit (2) from the dividend and append it to 43, then repeat: 432 / 53

Going ahead to step 5:
53 can be fit into 432 8 times, resulting in a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 578.0
Subtract 424 from 432 to get 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 53

Going ahead to step 6:
If we divide 81 by 53, we get 1 and a remainder of 28.
Record the quotient 1 as the next digit in the result. 
Result so far: 5781.0
Subtract 53 from 81 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 7:
The number 53 fits into 280 5 times, leaving a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 5781.5
Subtracting 265 from 280 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 8:
150 divided by 53 is 2 with a remainder of 44.
Record the quotient 2 as the next digit in the result. 
Result so far: 5781.52
If we take 106 away from 150, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 9:
440 divided by 53 is 8 with a remainder of 16.
Write down 8 as next digit of the result. 
Result so far: 5781.528
Subtract 424 from 440 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 10:
The number 53 fits into 160 3 times, leaving a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 5781.5283
The remainder is 1 after subtracting 159 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 11:
When dividing 10 by 53, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 5781.5283
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 12:
When dividing 100 by 53, we get 1 with a remainder of 47.
Put 1 as the next digit of the answer. 
Result so far: 5781.528301
Subtract 53 from 100 to get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Step 13:
53 goes into 470 8 times with a remainder of 46.
Put 8 as the next digit of the answer. 
Result so far: 5781.5283018
Subtracting 424 from 470 leaves us with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Going ahead to step 14:
If we divide 460 by 53, we get 8 and a remainder of 36.
Record the quotient 8 as the next digit in the result. 
Result so far: 5781.52830188
Deduct 424 from 460 and we're left with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

In conclusion, the division gives 5781.52830188 with a balance of 3.6e-08.