We look at the division of 377357 by 71 
Our goal is to divide 377357 by 71.

Advancing to step 1:
If we divide 3 by 71, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 71

Step 2:
71 can be fit into 37 0 times, resulting in a remainder of 37.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 37, we end up with 37.
Take the next digit (7) from the dividend and append it to 37, then repeat: 377 / 71

Step 3:
When dividing 377 by 71, we get 5 with a remainder of 22.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 355 from 377 leaves us with 22.
Bring next digit (3) of the dividend behind the 22 and repeat the process: 223 / 71

Moving on to step 4:
223 divided by 71 is 3 with a remainder of 10.
Record the quotient 3 as the next digit in the result. 
Result so far: 53.0
Deduct 213 from 223 and we're left with 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 71

On to step 5:
The number 71 fits into 105 1 times, leaving a remainder of 34.
The number 1 becomes the next digit in our result. 
Result so far: 531.0
If we subtract 71 from 105, we get 34.
Append the next digit (7) from the dividend to 34 and continue with: 347 / 71

Going ahead to step 6:
If we divide 347 by 71, we get 4 and a remainder of 63.
Use 4 as the next digit of our solution. 
Result so far: 5314.0
Subtract 284 from 347 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.

Advancing to step 7:
71 goes into 630 8 times with a remainder of 62.
Put 8 as the next digit of the answer. 
Result so far: 5314.8
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 8:
When dividing 620 by 71, we get 8 with a remainder of 52.
Put 8 as the next digit of the answer. 
Result so far: 5314.88
If we subtract 568 from 620, we 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 5314.88 with a balance of 0.052.