CBSE Class 10 Answered
for a natural number n the number 8raiseto n can never end with the digit-------
Asked by | 14 May, 2011, 12:00: AM
Expert Answer
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
Answered by | 14 May, 2011, 02:52: PM
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