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 = 3ⁿ × 5ⁿ

The fundamental theorem of arithmetic states that every composite number has a unique prime factorization.  

∴ 15ⁿ can never end in 0 or 5.