show that 12n cannot end with the digit 0 or for any natural number n.
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If 12n ends with the digit zero it must be divisible by 5. This is possible only if prime factorisation of 12n contains the prime number 5. This is possible only if prime factorisation of 12n contains the prime number 5. Hence, there is no value of n e N for which 12n ends with digit zero or five.
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