31766 ÷ 4 = 7941 R2
Alright, let's work through the division of 31766 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 (1) of the dividend behind the 3 and repeat the process: 31 / 4

Step 2:
4 goes into 31 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 28 from 31 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 3:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 79
Subtract 36 from 37 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 4

Step 4:
4 goes into 16 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 794
Subtract 16 from 16 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 5:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 7941
Subtract 4 from 6 to get 2.

The final result is 7941 with a remainder of 2.