421157 ÷ 71 
We want to figure out the number of times 421157 can be divided by 71.

On to step 1:
71 can be fit into 4 0 times, resulting in a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 71

Step 2:
The number 71 fits into 42 0 times, leaving a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 42 and we're left with 42.
Take the next digit (1) from the dividend and append it to 42, then repeat: 421 / 71

Let's proceed to step 3:
The number 71 fits into 421 5 times, leaving a remainder of 66.
Put 5 as the next digit of the answer. 
Result so far: 5.0
The remainder is 66 after subtracting 355 from 421.
Grab the next digit (1) from the dividend, add it to 66, then carry on: 661 / 71

Moving on to step 4:
71 can be fit into 661 9 times, resulting in a remainder of 22.
Use 9 as the next digit of our solution. 
Result so far: 59.0
If we subtract 639 from 661, we get 22.
Take the next digit (5) from the dividend and append it to 22, then repeat: 225 / 71

On to step 5:
The number 71 fits into 225 3 times, leaving a remainder of 12.
Record the quotient 3 as the next digit in the result. 
Result so far: 593.0
If we subtract 213 from 225, we get 12.
Append the next digit (7) from the dividend to 12 and continue with: 127 / 71

Moving on to step 6:
If we divide 127 by 71, we get 1 and a remainder of 56.
Write down 1 as next digit of the result. 
Result so far: 5931.0
If we subtract 71 from 127, we get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Step 7:
71 can be fit into 560 7 times, resulting in a remainder of 63.
The next digit of our result is 7. 
Result so far: 5931.7
Subtract 497 from 560 to get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Step 8:
71 goes into 630 8 times with a remainder of 62.
The next digit of our result is 8. 
Result so far: 5931.78
Subtract 568 from 630 to get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Moving on to step 9:
When dividing 620 by 71, we get 8 with a remainder of 52.
The number 8 becomes the next digit in our result. 
Result so far: 5931.788
Subtract 568 from 620 to get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

In conclusion, the division gives 5931.788 with a balance of 0.0052.