show that 12th cannot end with the digit 0 or 5 for any natural number n
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3
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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.
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.
Answered by
2
12 can not end in 0 and 5 because
12 has the foctor only 2,6
12=2*6
it not has the factor 2n*5m
Hence it will not end with 0
12 has the foctor only 2,6
12=2*6
it not has the factor 2n*5m
Hence it will not end with 0
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