14001 ÷ 2 = 7000 R1
Alright, let's work through the division of 14001 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 (0) of the dividend behind the 0 and repeat the process: 0 / 2

Step 3:
2 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 70
Subtract 0 from 0 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 2

Step 4:
2 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 700
Subtract 0 from 0 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 2

Step 5:
2 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 7000
Subtract 0 from 1 to get 1.

The final result is 7000 with a remainder of 1.