37590 ÷ 9 = 4176 R6
Alright, let's work through the division of 37590 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 (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 3:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 41
Subtract 9 from 15 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 9

Step 4:
9 goes into 69 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 417
Subtract 63 from 69 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 9

Step 5:
9 goes into 60 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 4176
Subtract 54 from 60 to get 6.

The final result is 4176 with a remainder of 6.