Question

Check whether 15*n can end with digit zero for any natural number

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.

Hope it helps

Answer 2

As we know that

15n = (3 x 5)n

 =  3n x 5n

The prime factorization of 15 doesn't have a 2 and 5 as its factor. So, its factorization will never end in 10 as a number ending in 10 must have a factors as 5 and 2. So, 15n will never end in zero as 15 doesn't has 2 as a factor.