3873 ÷ 4 = 968 R1
Alright, let's work through the division of 3873 by 4 step by step.

Step 1:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 4

Step 2:
4 goes into 38 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 36 from 38 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 4

Step 3:
4 goes into 27 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 96
Subtract 24 from 27 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 4

Step 4:
4 goes into 33 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 968
Subtract 32 from 33 to get 1.

The final result is 968 with a remainder of 1.