7677 ÷ 4 = 1919 R1
Alright, let's work through the division of 7677 by 4 step by step.

Step 1:
4 goes into 7 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 7 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 4

Step 2:
4 goes into 36 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 36 from 36 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 4

Step 3:
4 goes into 7 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 191
Subtract 4 from 7 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 4:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 1919
Subtract 36 from 37 to get 1.

The final result is 1919 with a remainder of 1.