Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

SIR

  • one year ago

N=12*12*12*3*3*3*3*5*5,then the total number of even factor of N is

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

    Split the number N into prime factors and then obtain the even factors using simple combinatorics. I see 126 unique even divisors.

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

    \[ N=2^6 3^7 5^2 \]

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

    To have an even factor the 2 must always occur in the factor. So the even factors are of the form \[ 2^m 3^n 5^p; \quad 1\leq m \leq 6; \quad 0\leq n \leq 7; \quad 0\leq m \leq 2 \] How many are there?

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

    There are 6* 8* 3= 144

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

    Here a list of the 144 {2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 32, 36, 40, 48, 50, 54, 60, \ 64, 72, 80, 90, 96, 100, 108, 120, 144, 150, 160, 162, 180, 192, 200, \ 216, 240, 270, 288, 300, 320, 324, 360, 400, 432, 450, 480, 486, 540, \ 576, 600, 648, 720, 800, 810, 864, 900, 960, 972, 1080, 1200, 1296, \ 1350, 1440, 1458, 1600, 1620, 1728, 1800, 1944, 2160, 2400, 2430, \ 2592, 2700, 2880, 2916, 3240, 3600, 3888, 4050, 4320, 4374, 4800, \ 4860, 5184, 5400, 5832, 6480, 7200, 7290, 7776, 8100, 8640, 8748, \ 9720, 10800, 11664, 12150, 12960, 14400, 14580, 15552, 16200, 17496, \ 19440, 21600, 21870, 23328, 24300, 25920, 29160, 32400, 34992, 36450, \ 38880, 43200, 43740, 46656, 48600, 58320, 64800, 69984, 72900, 77760, \ 87480, 97200, 109350, 116640, 129600, 139968, 145800, 174960, 194400, \ 218700, 233280, 291600, 349920, 388800, 437400, 583200, 699840, \ 874800, 1166400, 1749600, 3499200}

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.