Question

Show that 15^n cannot end with the digits 0 for any natural number n.

Answer 1

if the number 15^n ,for any natural number n were to end with digit zero , then it would be divisible by 5 or 2

i.e it should contain the primes 5 and 2 but this is not possible since 15^n = ( 3 into 5)^n

the uniqueness of the fundamental theorem of arithemetic guarantees that there are no other primes in the factorisation of 15^n. so there is no natural number for which 15^n ends with digit 0