2277 ÷ 6 = 379 R3
No problem, we've got 2277 and 6 for the division.

Step 1:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 2:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 18 from 22 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 6

Step 3:
6 goes into 47 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 37
Subtract 42 from 47 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 4:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 379
Subtract 54 from 57 to get 3.

The final result is 379 with a remainder of 3.