1.Show that 15" cannot end with the digit zero for any natural number

1.	1.Show that 15" cannot end with the digit zero for any natural number n.
Answer» 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.

1.Show that 15" cannot end with the digit zero for any natural number n.

Answer»

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.