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A Prime number is a positive integer with two factors: one and the number itself. If you test the numbers up to the square root and your number is not divisible by any of them, it's prime.
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Can you determine whether 1009 a prime?
Yes, it is.
Determine whether 2 is a prime compositive or neither?
2 is prime.
Determine whether 24 is prime or composite?
It's composite
How can you use the prime factorization of two numbers to determine whether they are relative prime?
If the prime factorizations have no prime factors in common, the numbers are relatively prime.
How can you use the prime factorization of two numbers to determine whether they are relatively prime?
Use the prime factorizations to determine the GCF. If the GCF is 1, the numbers are relatively prime. If the two numbers have no prime factors in common, they are relatively prime.
How can you use prime factorization to determine whether two numbers are relatively prime?
If the prime factorizations contain no factors in common (their GCF is 1), the numbers are relatively prime.
How can you use the prime factorization to determine whether 35 is a factor of the number?
If the prime factorization contains a 5 and a 7, 35 is a factor.
How can you determine whether the gcf of two numbers is one by looking at their prime factorizations?
If there are no prime factors in common, the GCF is 1.
How do mathematicians determine whether or not really large numbers are prime?
A primality test is an algorithm for determining whether an input number is prime, but I'm willing to bet that a lot of mathematicians type "prime number calculator" into their web browsers.
How can you determine from the prime factorization whether the least common multiple of two numbers is the product of the numbers?
If the prime factorizations have no factors in common, the LCM is the product of them.
Is the set of prime numbers well defined or not?
Well, there is a clear definition, and at least in theory you can always determine whether a number is a primer number or not, so I would say, yes.
How can you use the prime factorization of a number to determine whether the number is even or add?
Very easily: if the prime factorization includes 2, it's even. If not, it's odd.
