Question

Show that 15n cannot end with the digit 2 for any natural number

Answer 1

15n cannot end with digit 2 becoz 15 is not devisible by 2.
15=3×5, 2 is not a factor of 15.
so 15n cannot end with digit 2.


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Answer 2

Answer:

(15) ^n =(3×5) ^n

=3^n×5^n

if (15) ^n is to end with digit 2 for any natural number, then

(15) ^n is divisible by 2

therefore 2 must be the prime factor of (15) ^n

but in the prime factorisation of (15) ^n , 2 down not occur as it's prime factor.

therefore (15) ^n cannot end with digit 2