Q. 133.8( 10 Votes )

Prove that 9n cannot end with 0.

Answer :

Given: 9n


To prove: 9n cannot end with 0.


Explanation:


We know all the composite numbers which ends with 0 have 10 as a factor.


So, this implies here for composite number 9, 10 is factor of 9n.


We have for any natural number p:


9n = 10 × p


(3× 3) n = 2 × 5× p


3n × 3n = 2 × 5× p


That is 5 is prime factor of 3n × 3n which is not possible.


Thus, our assumption is wrong.


Hence 9n cannot end with 0.


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