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Show that 12th cannot end with …

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Show that 12th cannot end with digit 0 or 5 for any natural number 'n'

    • Posted by Neha Duggal 6 years, 11 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Arohi . 6 years, 11 months ago

    If 12n ends with 0 then it must have 5 as a factor. But, 12n=(2×2×3)n which shows that only 2 and 3 are the prime factors of 12n. Also, we know from the fundamental theory of arithmetic that the prime factorization of each number is unique. So, 5 is not a factor of 12n. Hence, 12n can never end with the digit 0.

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