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Thread: Greatest Possible Length

  1. #1
    Super Member harpazo's Avatar
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    Greatest Possible Length

    For any positive integer n, n > 1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5). Given this information, what is the greatest possible length of a positive integer less than 1,000?

    A. 10
    B. 9
    C. 8
    D. 7
    E. 6


    The only number that evenly divided 1,000 from the list given is 10. So, I selected A as my answer. The correct answer, however, is B. Why is B right?
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  2. #2
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    Re: Greatest Possible Length

    The smallest number with a "length" of 10 would be 2x2x2x2x2x2x2x2x2x2 = 2^10 =1024 which is greater than 1000. So a number less than 1000 could not have a length of 10.

    2^9 =512 which is smaller than 1000.


    Therefore, the "greatest length of a positive integer less than 1000" is 9.

    The only number that evenly divided 1,000 from the list given is 10. So, I selected A as my answer.
    The fact that 10 divides evenly into 1000 (so does 8, by the way) has nothing to do with the question.
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  3. #3
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    Re: Greatest Possible Length

    Quote Originally Posted by harpazo View Post
    1 Thessalonians 4:16-18
    For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first: 17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord. 18 Wherefore comfort one another with these words.
    Apostle Paul
    Hey Harpy, that's real funny...that guy Paul is a hecka good comedian!

    Who is the archangel: Plato or Hallsofivy?
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  4. #4
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    Re: Greatest Possible Length

    Oh, dear. I don't think I have every been mistaken for an angel!
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  5. #5
    Super Member harpazo's Avatar
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    Re: Greatest Possible Length

    Quote Originally Posted by DenisB View Post
    Hey Harpy, that's real funny...that guy Paul is a hecka good comedian!

    Who is the archangel: Plato or Hallsofivy?
    Paul is describing the rapture of the church in this passage. In the original Greek, the words "caught up" written as harpazo, means to be quickly remove or violently snatched. The words of Paul are real, just as real as the person we are in every sense. In fact, several rapture events took place in both the Old and New Testaments. The BIG DIFFERENCE between removing one or two individuals will be the massive removal of millions of people around the globe. The rapture will take place because the Bible can be trusted.
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