14180 ÷ 9 = 1575 R5
Alright, let's work through the division of 14180 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 (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: 157
Subtract 63 from 68 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 9

Step 5:
9 goes into 50 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 1575
Subtract 45 from 50 to get 5.

The final result is 1575 with a remainder of 5.