37581 ÷ 9 = 4175 R6
Alright, let's work through the division of 37581 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 (8) of the dividend behind the 6 and repeat the process: 68 / 9

Step 4:
9 goes into 68 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 417
Subtract 63 from 68 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 9

Step 5:
9 goes into 51 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 4175
Subtract 45 from 51 to get 6.

The final result is 4175 with a remainder of 6.