Question
Sun May 15, 2011 By:

for a natural number n. the number 8raiseto n can never end with the digit execpt zero

Expert Reply
Mon May 16, 2011

Let 8n ends with 0

=> 8n = 10a  ( where a is any natural no)

8n = 2 x 5 x a

 => 8n has 2 and 5 as its prime factors  . . . . . . .(1)

But fundamental theorem of arithmetic states that 8n can only have two as its prime factors [Since, 8n = (2 x 2 x 2)n ]  . . . .(2)

Thus, from (1) and (2), it can be said  that our supposition is wrong.

Hence 8n can never end with 0.

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