Question

Show that 4^n can never end with the digit zero for any natural number n.

Answer 1

A number ending with zero is also divisible by 5.
Therefore 4^nmust be divisible by 5
If 4^n is divisible by 5 then by using theorem we can show that 4is also divisible by5.
But it is not so.
Thus 4^n is not divisible by 5.
Hence proved

Answer 2

Any number to end with 0 must be divisible by 2 and 5 .

Since, 4 is divisible by 2, but not by 5.

Therefore, any number of the form 4^n can never end with the digit 0.

Hence,proved.