Question

Check whether 15^n can end with the digit zero for any natural number n.

Answer 1

If 15ⁿ end with digit zero,then the number should be divisible by 2 and 5.

As 2×5=10

→This means the prime factorization of 15ⁿ should contain prime factors 2 and 5.

→15ⁿ = (3×5)ⁿ

It does not have the prime factor 2 but have 3 and 5,

Since 2 is not present in the prime factorization, there is no natural number nor which 15ⁿ ends with digit zero.

So,15ⁿ can not end with digit zero.