Question

Which of the following numbers cannot end with zero for any natural number $n$ ?

• A. $4^n$
• B. $6^n$
• C. ${20}^n$
• D. $5^n$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $4^n$
B $6^n$
D $5^n$

For $a^n$ to end with digit zero for any natural number n, it should be divisible by both 2 and 5. This means that the prime factorisation of $a^n$ should contain the prime numbers 2 and 5.
$4=2^2,$
$6=2\times 3,$
$20=2^2\times 5$ and
$5=1\times 5.$
Only 20 has both 2 and 5 in its prime factorisation.
Hence, for a natural number $n,{20}^n$ can end with zero.
$4^n,6^n$ and $5^n$ cannot end with zero for any natural number $n.$