Question 344032: Jim and his study group want to know if 601 is a prime or composite number. He explained to his group that neither 2,3,4 nor 5 were factors of 601 by using divisibilty rules. Mary claims that they did not have to check 4 since they all ready knew 2 was not a factor, but Jim disagreed. Jim claimed that it was possible for 4 to be a factor of a number even if 2 wasnt.
Is jims claim correct? Explain?
List all of the prime numbers you would check to see if they were factors when trying to determine if 601 is a prime or composite number. Explain why your list is complete and efficent.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Jim and his study group want to know if 601 is a prime or composite number. He explained to his group that neither 2,3,4 nor 5 were factors of 601 by using divisibilty rules. Mary claims that they did not have to check 4 since they all ready knew 2 was not a factor, but Jim disagreed. Jim claimed that it was possible for 4 to be a factor of a number even if 2 wasnt.
Is jims claim correct? No, Jim is wrong.
Explain? If any number is divisible by 4, it's 4*n. 4n is divisible by 2.
All even factors can be crossed off if it's not divisible by 2.
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List all of the prime numbers you would check to see if they were factors when trying to determine if 601 is a prime or composite number. Explain why your list is complete and efficent.
You need to try all prime numbers < sqrt(601).
2,3,5,7,11,13,17,19,23 and 29
It's not necessary to try prime numbers higher that sqrt(601), because any divisor more than that would give a quotient less than sqrt(601), which you've already tried.
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