Question

12. Can the number 6, n being a natural number, end with the digit 5? Give reasons.
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Answer 1

Answer:

For any number ending with 5 the prime factor 5 should be there in its primefactorisation (for eg: 5=5,15=3x5,25=5x5). ... But 6n has only 2 and 3 as prime factors.So 6n can never end with digit 5 for any natural number n.

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Answer 2

Answer:

the number 6n, if ends with 5

=> it's prime factor must be 5

but prime factors of 6n=(2×3)n

accounting to fundamental theorem of arithimatic,

there can't be any other prime factor than 2n and 3n .

=>the number 6, n being a natural number, can't end with the digit 5