34079 ÷ 9 = 3786 R5
Alright, let's work through the division of 34079 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 (4) of the dividend behind the 3 and repeat the process: 34 / 9

Step 2:
9 goes into 34 3 times with a remainder of 7.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 27 from 34 to get 7.
Bring next digit (0) of the dividend behind the 7 and repeat the process: 70 / 9

Step 3:
9 goes into 70 7 times with a remainder of 7.
Write down 7 as next digit of of the result. 
Result so far: 37
Subtract 63 from 70 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 9

Step 4:
9 goes into 77 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 378
Subtract 72 from 77 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 9

Step 5:
9 goes into 59 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 3786
Subtract 54 from 59 to get 5.

The final result is 3786 with a remainder of 5.