31373 ÷ 9 = 3485 R8
Alright, let's work through the division of 31373 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 (3) of the dividend behind the 4 and repeat the process: 43 / 9

Step 3:
9 goes into 43 4 times with a remainder of 7.
Write down 4 as next digit of of the result. 
Result so far: 34
Subtract 36 from 43 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 9

Step 4:
9 goes into 77 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 348
Subtract 72 from 77 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 9

Step 5:
9 goes into 53 5 times with a remainder of 8.
Write down 5 as next digit of of the result. 
Result so far: 3485
Subtract 45 from 53 to get 8.

The final result is 3485 with a remainder of 8.