31065 ÷ 9 = 3451 R6
Alright, let's work through the division of 31065 by 9 step by step.

Step 1:
9 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 / 9

Step 2:
9 goes into 31 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 27 from 31 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 9

Step 3:
9 goes into 40 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 34
Subtract 36 from 40 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 9

Step 4:
9 goes into 46 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 345
Subtract 45 from 46 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 5:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 3451
Subtract 9 from 15 to get 6.

The final result is 3451 with a remainder of 6.