31777 ÷ 8 = 3972 R1
Alright, let's work through the division of 31777 by 8 step by step.

Step 1:
8 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 (1) of the dividend behind the 3 and repeat the process: 31 / 8

Step 2:
8 goes into 31 3 times with a remainder of 7.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 24 from 31 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 8

Step 3:
8 goes into 77 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 39
Subtract 72 from 77 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 4:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 397
Subtract 56 from 57 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 8

Step 5:
8 goes into 17 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 3972
Subtract 16 from 17 to get 1.

The final result is 3972 with a remainder of 1.