77663 ÷ 4 = 19415 R3
Alright, let's work through the division of 77663 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 (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 2:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 36 from 37 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 3:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 194
Subtract 16 from 16 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 4:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1941
Subtract 4 from 6 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 5:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 19415
Subtract 20 from 23 to get 3.

The final result is 19415 with a remainder of 3.