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Show that 9n cannot end with …

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Show that 9n cannot end with zero for any natural number n

Posted by Pragati Kumari 7 years, 7 months ago

CBSE > Class 10 > Mathematics

3 answers

Vaishnavi Singh 7 years, 7 months ago

If 9n ends with 0 then it must have 5 as a factor. But 9n has factor of (3.3)n =(3n.3n) which shows that 3 is the only factor of 9n. We know the fundamental theorem of arithematic ie. (5m.2n) and 9n does not apply on 9n. So, 9n can never end with zero.

2Thank You

Anant Yadav 7 years, 7 months ago

It can be written in the form of 3n^2. So to end with 0 it should have 5 as a prime factor but clearly it does not have any so it cannot end with 0

1Thank You

Susmit Mishra 7 years, 7 months ago

9n= 3^2n the prime factorisation does not contain 10 and it is unique so 9n deos not end with zero

5Thank You

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