10416 ÷ 9 = 1157 R3
Alright, let's work through the division of 10416 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 (0) of the dividend behind the 1 and repeat the process: 10 / 9

Step 2:
9 goes into 10 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 10 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 9

Step 3:
9 goes into 14 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 9 from 14 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 9

Step 4:
9 goes into 51 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 115
Subtract 45 from 51 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

Step 5:
9 goes into 66 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 1157
Subtract 63 from 66 to get 3.

The final result is 1157 with a remainder of 3.