14338 ÷ 2 = 7169 R0
Alright, let's work through the division of 14338 by 2 step by step.

Step 1:
2 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 / 2

Step 2:
2 goes into 14 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 14 from 14 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 2

Step 3:
2 goes into 3 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 71
Subtract 2 from 3 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 2

Step 4:
2 goes into 13 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 716
Subtract 12 from 13 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 2

Step 5:
2 goes into 18 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 7169
Subtract 18 from 18 to get 0.

The final result is 7169 with a remainder of 0.