We're dividing 377765 by 81 
We want to divide 377765 by 81.

On to step 1:
81 goes into 3 0 times with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 81

Step 2:
The number 81 fits into 37 0 times, leaving a remainder of 37.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 37, we end up with 37.
Fetch the next digit (7) from the dividend, attach it to 37 and continue: 377 / 81

Going ahead to step 3:
81 goes into 377 4 times with a remainder of 53.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 324 away from 377, we end up with 53.
Bring next digit (7) of the dividend behind the 53 and repeat the process: 537 / 81

On to step 4:
If we divide 537 by 81, we get 6 and a remainder of 51.
Record the quotient 6 as the next digit in the result. 
Result so far: 46.0
Subtracting 486 from 537 leaves us with 51.
Take the next digit (6) from the dividend and append it to 51, then repeat: 516 / 81

On to step 5:
If we divide 516 by 81, we get 6 and a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 466.0
Subtract 486 from 516 to get 30.
Include the next digit (5) from the dividend after 30, then repeat: 305 / 81

Advancing to step 6:
If we divide 305 by 81, we get 3 and a remainder of 62.
Record the quotient 3 as the next digit in the result. 
Result so far: 4663.0
The remainder is 62 after subtracting 243 from 305.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 7:
If we divide 620 by 81, we get 7 and a remainder of 53.
The next digit of our result is 7. 
Result so far: 4663.7
Deduct 567 from 620 and we're left with 53.
Since there are no more digits in the dividend, we add a zero to the remainder making it 530, and continue the process.

Going ahead to step 8:
If we divide 530 by 81, we get 6 and a remainder of 44.
The number 6 becomes the next digit in our result. 
Result so far: 4663.76
The remainder is 44 after subtracting 486 from 530.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 9:
The number 81 fits into 440 5 times, leaving a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 4663.765
Subtracting 405 from 440 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 10:
If we divide 350 by 81, we get 4 and a remainder of 26.
Record the quotient 4 as the next digit in the result. 
Result so far: 4663.7654
Deduct 324 from 350 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 11:
81 goes into 260 3 times with a remainder of 17.
Use 3 as the next digit of our solution. 
Result so far: 4663.76543
Deduct 243 from 260 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Advancing to step 12:
When dividing 170 by 81, we get 2 with a remainder of 8.
The next digit of our result is 2. 
Result so far: 4663.765432
If we take 162 away from 170, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 13:
81 can be fit into 80 0 times, resulting in a remainder of 80.
The number 0 becomes the next digit in our result. 
Result so far: 4663.765432
The remainder is 80 after subtracting 0 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Step 14:
The number 81 fits into 800 9 times, leaving a remainder of 71.
Record the quotient 9 as the next digit in the result. 
Result so far: 4663.76543209
Deduct 729 from 800 and we're left with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

In conclusion, the division gives 4663.76543209 with a balance of 7.1e-08.