Question

Check whether the number 15ⁿ, where n is a natural number, can end with the digit 0.

Answer 1

Theorem: Every composite number can be decomposed as a product prime numbers in a unique way, except for the order.

Step 1: Factorize 15ⁿ

15ⁿ = (3 × 5)ⁿ = 3ⁿ × 5ⁿ

Step 2:

Prime factorization of 15 does not have a 2 and 5 as its factor.

Factorization will end in 10 as a number ending in 10 must have factors as 5 and 2.

Hence, 15ⁿ will never end in zero.