Question

Consider the number 12ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 12ⁿ ends with the digital zero.

Answer 1

We know if any number ends with the digit zero it is always divisible by 5.

If 12ⁿ ends with the digit zero, it must divisible by 5.

This is possible only if prime factorisation of 12ⁿ contains the prime number 5.

Now, 12 = 2 x 2 x 3 = 2² x 3

⇒ 12ⁿ = (2² x 3)ⁿ = 2²ⁿ x 3ⁿ

i.e., prime factorisation of 12ⁿ does not contain the prime number 5.

⇒ There is no value of n ∈ N for which 12ⁿ ends with the digit zero.