37088 ÷ 9 = 4120 R8
Alright, let's work through the division of 37088 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 (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 2:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 37 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 9

Step 3:
9 goes into 10 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 41
Subtract 9 from 10 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 9

Step 4:
9 goes into 18 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 412
Subtract 18 from 18 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 9

Step 5:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of of the result. 
Result so far: 4120
Subtract 0 from 8 to get 8.

The final result is 4120 with a remainder of 8.