37259 ÷ 9 = 4139 R8
Alright, let's work through the division of 37259 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 (2) of the dividend behind the 1 and repeat the process: 12 / 9

Step 3:
9 goes into 12 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 41
Subtract 9 from 12 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 9

Step 4:
9 goes into 35 3 times with a remainder of 8.
Write down 3 as next digit of of the result. 
Result so far: 413
Subtract 27 from 35 to get 8.
Bring next digit (9) of the dividend behind the 8 and repeat the process: 89 / 9

Step 5:
9 goes into 89 9 times with a remainder of 8.
Write down 9 as next digit of of the result. 
Result so far: 4139
Subtract 81 from 89 to get 8.

The final result is 4139 with a remainder of 8.