14638 ÷ 9 = 1626 R4
Let's divide 14638 by 9.

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 (6) of the dividend behind the 5 and repeat the process: 56 / 9

Step 3:
9 goes into 56 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 54 from 56 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 9

Step 4:
9 goes into 23 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 162
Subtract 18 from 23 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 9

Step 5:
9 goes into 58 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 1626
Subtract 54 from 58 to get 4.

The final result is 1626 with a remainder of 4.