We're dividing 377355 by 78 
We want to figure out the number of times 377355 can be divided by 78.

Advancing to step 1:
3 divided by 78 is 0 with a remainder of 3.
The next digit of our result is 0. 
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 / 78

Going ahead to step 2:
37 divided by 78 is 0 with a remainder of 37.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 37 leaves us with 37.
Fetch the next digit (7) from the dividend, attach it to 37 and continue: 377 / 78

Moving on to step 3:
377 divided by 78 is 4 with a remainder of 65.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we subtract 312 from 377, we get 65.
Fetch the next digit (3) from the dividend, attach it to 65 and continue: 653 / 78

Moving on to step 4:
The number 78 fits into 653 8 times, leaving a remainder of 29.
The number 8 becomes the next digit in our result. 
Result so far: 48.0
Deduct 624 from 653 and we're left with 29.
Bring next digit (5) of the dividend behind the 29 and repeat the process: 295 / 78

Let's proceed to step 5:
When dividing 295 by 78, we get 3 with a remainder of 61.
Use 3 as the next digit of our solution. 
Result so far: 483.0
Deduct 234 from 295 and we're left with 61.
Take the next digit (5) from the dividend and append it to 61, then repeat: 615 / 78

Let's proceed to step 6:
The number 78 fits into 615 7 times, leaving a remainder of 69.
The next digit of our result is 7. 
Result so far: 4837.0
Deduct 546 from 615 and we're left with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Going ahead to step 7:
78 can be fit into 690 8 times, resulting in a remainder of 66.
The number 8 becomes the next digit in our result. 
Result so far: 4837.8
The remainder is 66 after subtracting 624 from 690.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Advancing to step 8:
If we divide 660 by 78, we get 8 and a remainder of 36.
Record the quotient 8 as the next digit in the result. 
Result so far: 4837.88
If we take 624 away from 660, we end up 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.

The quotient of the division is 4837.88, and the remainder is 0.036.