Question

Prove that there is no natural number for which 15 to the power n ends with the digit zero.

Answer 1

15 to the power of 1 may be the answer

Answer 2

let us assume that 15^n can end with digit zero for any natural no. n 
therefore, 2 is factor of 15^n
now, 15^n = (3*5)^n = 3^n * 5^n
so, 3 and 5 are factors of 15^n

the uniqueness of fundamental theorem of arithmetic says that there are no other primes  in the factorization of 15^n.

hence,  our supposition is wrong.
thus, 15^n can never end with digit zero for any natural number  n.




hope this help you!! :)