NCERT · Class 10 · Mathematics · Real NumbersCheck whether 6ⁿ can end with the digit 0 for any natural number n.

If the number 6ⁿ were to end with the digit zero, it would be divisible by 5. This means that the prime factorization of 6ⁿ would contain the prime number 5. However, the prime factorization of 6ⁿ is (2 × 3)ⁿ = 2ⁿ × 3ⁿ. This shows that the only primes in the factorization of 6ⁿ are 2 and 3. By the uniqueness of the Fundamental Theorem of Arithmetic, there is no other prime in the factorization. Hence, 6ⁿ can never end with the digit 0.