Prove that 9n cannot end with 0.

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of Arithmetic41 mins
Fundamental Theorem of Arithmetic- 143 mins
NCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Euclids Division Lemma49 mins
Quiz | Imp Qs on Real Numbers37 mins
Interactive Quiz - HCF and LCM32 mins
Application of Euclids Division Lemma50 mins
Relation Between LCM , HCF and Numbers46 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses