Q19 of 30 Page 36

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

If 15n is divisible by 10 then it can end with digit zero


If it is divisible by 10 it has to be divisible by 5 and 2 both


The prime factorization of 15 is 3 × 5


⇒ 15n = (3 × 5)n


Observe that (3 × 5)n is divisible by 5 (because and 3n × 5n–1 is integer for n>1) but not by 2 because no 2 of in primethe factorization of 15


Hence 15n is not divisible by 10


Hence 15n does not end with 0 for any natural number n


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