A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

vera_ewing

  • one year ago

How do you solve this?

  • This Question is Closed
  1. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A particular integer N is divisible by two different prime numbers p and q. Which of the following must be true? I. N is not a prime number. II. N is divisible by pq. III. N is an odd integer.

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you know what a prime number is?

  3. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A number that can only be divided by 1 and itself.

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes so what do you think the answer is

  5. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Well if the prime numbers p and q were 2 and 3, respectively, then that means I. would be incorrect right?

  6. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Because then N would be 18, which is not a prime number.

  7. vera_ewing
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ohh wait so I. would be correct! Right? @freckles

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  9. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    would there be any other options though ? for example if p and q are 2 and 3 respectively then you could say one possibly for N is 2(3)=6 doesn't 2(3) go into N=6? Also don't you mean I would be correct?

  10. Here_to_Help15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    First, recall that a prime number is only divisible by itself and 1, and that 1 is not a prime number. So, statement I must be true, since a number that can be divided by two prime numbers can’t itself be prime. Next, recall that every number can be written as a product of a particular bunch of prime numbers. Let’s say that N is divisible by 3 and 5. Then, N is equal to 3 ·5 ·p1 ·p2 · · ·, where p1, p2, etc. are some other primes. So, N is divisible by 3 · 5 = 15. Statement II must be true. Finally, remember that 2 is a prime number. So, N could be 6, since 6 = 2 · 3. Statement III isn’t always true.

  11. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Awesome explanation by @Here_to_Help15 :)

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    agree

  13. mathmath333
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if N is divisible by two different prime numbers p and q then \(\large \color{black}{\begin{align} N\leq p\times q, \ \{p,q\} \in \mathbb{P} \hspace{1.5em}\\~\\ \end{align}}\) so N cannot be a prime number

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I get it

  15. Here_to_Help15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 4

    Thanks :)

  16. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Here_to_Help15 Great explanation, just modify it this way (add the capitalized words): "Next, recall that every NON-PRIME number can be written as a product"

  17. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.