Question

Can the number (15)ⁿ, n being a natural number, end with the digit 0? Give reasons.

Answer 1

If 15¹⁵ ends with 0 or 5, then it must have 5 as a factor. 

But only prime factors of 15 are 3 and 5.

∴ 15ⁿ = (5 × 3) n

15ⁿ = 3ⁿ × 5ⁿ

By observing the prime factorization 3ⁿ × 5ⁿ, we see that the only prime factors present are 3 and 5

Conclusion

For a number to end in 0, it must have both 2 and 5 as prime factors. Since the prime factorization of (15)ⁿ does not contain the prime factor 2, it can never produce a factor of 10.

Therefore, (15)ⁿ cannot end with the digit 0 for any natural number n.