Question

Show that any number of the form 4ⁿ , n ϵ N can never end with the digit 0.

Answer 1

If 4ⁿ ends with 0, then it must have 5 as a factor. 

But we know the only prime factor of 4ⁿ is 2. 

Also we know from the fundamental theorem of arithmetic that prime factorization of each number is unique. 

Hence, 4ⁿ can never end with the digit 0.