Question

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Answer 1

Here, 6ⁿ = (2 × 3)ⁿ = 2ⁿ × 3ⁿ

∴ Only prime factorization of 6ⁿ are 2 and 3

But 6ⁿ, for any natural number n, ends with digit 0, then it must contain the prime numbers 5.

Hence, 6ⁿ can not end with digit 0 for any natural number 'n'.