here is the question.. Show that any number of the form 6x,xEN can never end with the digit 0.
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Let 6n ends with digit 0 .
Hence 5 must be a factor of 6n
Which is not possible because the prime factorisation of 6n is (2×3)n
The fundamental theorem of arithmetic guarantees that there is no other primes in the prime factorisation of 6n .so there is no natural number n for which 6n ends with digit 0.as to be the digit ending with 0 it must be a factor of 10 which is not possible in the case of the prime factorisation of 6n as it comprises of 2 and 3 but not 5.
Hence 5 must be a factor of 6n
Which is not possible because the prime factorisation of 6n is (2×3)n
The fundamental theorem of arithmetic guarantees that there is no other primes in the prime factorisation of 6n .so there is no natural number n for which 6n ends with digit 0.as to be the digit ending with 0 it must be a factor of 10 which is not possible in the case of the prime factorisation of 6n as it comprises of 2 and 3 but not 5.
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