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Question
Check whether 6n can end with the digit 0 for any natural number n.
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Solution
We know that
62 = (2 × 3)n
62 = 2n × 3n
i.e., In the prime factorisation of 6n, there is no factor 5.
The fundamental theorem of arithmetic states that any composite number may be written as a product of primes. This factorization is unique, regardless of the sequence in which the primes occur.
∴ Our assumption that 6n ends with digit 0, is wrong.
Thus, there does not exist any natural number n for which 6n ends with zero.
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Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all. |
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