Question

Check whether 6ⁿ can end with the digit 0 for any natural number n.

Answer 1

We know that

6² = (2 × 3)ⁿ

6² = 2ⁿ × 3ⁿ

i.e., In the prime factorisation of 6ⁿ, there is no factor 5.

The fundamental theorem of arithmetic states that any composite number may be written as a product of primes. This factorization is unique, regardless of the sequence in which the primes occur.

∴ Our assumption that 6ⁿ ends with digit 0, is wrong.

Thus, there does not exist any natural number n for which 6ⁿ ends with zero.