65775 ÷ 4 = 16443 R3
Alright, let's work through the division of 65775 by 4 step by step.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 4

Step 2:
4 goes into 25 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 24 from 25 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 4

Step 3:
4 goes into 17 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 164
Subtract 16 from 17 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 4

Step 4:
4 goes into 17 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 1644
Subtract 16 from 17 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 4

Step 5:
4 goes into 15 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 16443
Subtract 12 from 15 to get 3.

The final result is 16443 with a remainder of 3.