59137 ÷ 9 = 6570 R7
Alright, let's work through the division of 59137 by 9 step by step.

Step 1:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 9

Step 2:
9 goes into 59 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 54 from 59 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 9

Step 3:
9 goes into 51 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 65
Subtract 45 from 51 to get 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 9

Step 4:
9 goes into 63 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 657
Subtract 63 from 63 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 9

Step 5:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 6570
Subtract 0 from 7 to get 7.

The final result is 6570 with a remainder of 7.