We look at the division of 41278 by 76 
We're looking to find how many times 76 goes into 41278.

Advancing to step 1:
When dividing 4 by 76, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Grab the next digit (1) from the dividend, add it to 4, then carry on: 41 / 76

Moving on to step 2:
76 goes into 41 0 times with a remainder of 41.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 41, we get 41.
Grab the next digit (2) from the dividend, add it to 41, then carry on: 412 / 76

Moving on to step 3:
The number 76 fits into 412 5 times, leaving a remainder of 32.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Deduct 380 from 412 and we're left with 32.
Bring next digit (7) of the dividend behind the 32 and repeat the process: 327 / 76

Going ahead to step 4:
The number 76 fits into 327 4 times, leaving a remainder of 23.
Record the quotient 4 as the next digit in the result. 
Result so far: 54.0
If we subtract 304 from 327, we get 23.
Fetch the next digit (8) from the dividend, attach it to 23 and continue: 238 / 76

Going ahead to step 5:
238 divided by 76 is 3 with a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 543.0
If we subtract 228 from 238, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 6:
100 divided by 76 is 1 with a remainder of 24.
The number 1 becomes the next digit in our result. 
Result so far: 543.1
If we take 76 away from 100, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 7:
240 divided by 76 is 3 with a remainder of 12.
Put 3 as the next digit of the answer. 
Result so far: 543.13
Subtracting 228 from 240 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 8:
120 divided by 76 is 1 with a remainder of 44.
The number 1 becomes the next digit in our result. 
Result so far: 543.131
Deduct 76 from 120 and we're left 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:
76 can be fit into 440 5 times, resulting in a remainder of 60.
The next digit of our result is 5. 
Result so far: 543.1315
Subtracting 380 from 440 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 10:
76 can be fit into 600 7 times, resulting in a remainder of 68.
Record the quotient 7 as the next digit in the result. 
Result so far: 543.13157
If we subtract 532 from 600, we get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Advancing to step 11:
If we divide 680 by 76, we get 8 and a remainder of 72.
The number 8 becomes the next digit in our result. 
Result so far: 543.131578
Deduct 608 from 680 and we're left with 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Let's proceed to step 12:
76 goes into 720 9 times with a remainder of 36.
The number 9 becomes the next digit in our result. 
Result so far: 543.1315789
The remainder is 36 after subtracting 684 from 720.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Advancing to step 13:
If we divide 360 by 76, we get 4 and a remainder of 56.
Record the quotient 4 as the next digit in the result. 
Result so far: 543.13157894
The remainder is 56 after subtracting 304 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Our division results in 543.13157894 with a remaining 5.6e-08.