14109 ÷ 9 = 1567 R6
Alright, let's work through the division of 14109 by 9 step by step.

Step 1:
9 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 9

Step 2:
9 goes into 14 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 14 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: 15
Subtract 45 from 51 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 9

Step 4:
9 goes into 60 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 156
Subtract 54 from 60 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 9

Step 5:
9 goes into 69 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 1567
Subtract 63 from 69 to get 6.

The final result is 1567 with a remainder of 6.