Is -5 prime , Is (6)^1/2 Even ?
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-5 is not a prime as prime numbers are integers greater than 1.
Even numbers always end with a digit 0, 2, 4, 6, 8. And 6^(1/2) is a decimal so it is not an even number.
Even numbers always end with a digit 0, 2, 4, 6, 8. And 6^(1/2) is a decimal so it is not an even number.
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Another way that I look at prime numbers...
Prime number is a number where only has the number 1 and itself as its factors.
Therefore -5 has factors of -1 and 5, and if you want to include it, 1.
This means that -5 has one factor two many to be prime.
Prime number is a number where only has the number 1 and itself as its factors.
Therefore -5 has factors of -1 and 5, and if you want to include it, 1.
This means that -5 has one factor two many to be prime.
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That's like saying factors of 20 could be 20 and 1 so 20 is prime."Factors of -5 could be 1 and -5, which would satisfy the rule of 'factors of 1 and itself'
Is there something I'm forgetting?"
Just remember that negative numbers can never be prime because the true definition of prime isn't a number with "factors of 1 and itself," but instead a number with "two distinct natural number divisors". A natural number is 1,2,3,4,5..... 0 and neg integers are not natural numbers.
So with -5 what are two unique positive integers other than 0 that can multiply and create -5? You can't do it with just two. The only way is 5*1*-1, which does not satisfy the rule of (1) only two factors and (2) the only two factors of the number must be natural.
This is why 1 is NOT prime. What two UNIQUE natural numbers can you multiply together and get 1? Well you might say 1*1, but they are not unique, they are the same number, so 1 is not prime.
My illustration in the previous post may not be sufficient. But hopefully this clarifies with a bit more definitional jargon.
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