Question
Sat May 14, 2011 By:

for a natural number n the number 8raiseto n can never end with the digit-------

Expert Reply
Sat May 14, 2011

let 8n ends with 0

=> 8n = 10a  ( where a is any natural no., 10a is the general form for all the numbers which end in 0 )

8n = 2 x 5 x a

 

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

but fundamental theorm of arithmetic states that 8n can only have two as its prime factors [ b'cos 8n = (2 x 2 x 2)n . . . .(2)

so by contradiction, our suppostition is wrong

hence 8n can never end with 0

 

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